I think you are both on the right track here.
The largest/heaviest paleozoic animals were likely giant eugeneodontid holocephalans (such as
Edestus,
Helicoprion and
Parahelicoprion). Some of them probably exceeded the 10 m mark in the Permian, making it unlikely any known arthrodiran (I heard statements of
Titanichthys, a filter-feeder, probably growing slightly larger than
Dunkleosteus, but didn’t verify them), stem-tetrapod, Batrachomorph, Amniote or other animal of the Palaeozoic reached similar sizes.
The key aspect to consider is that
almost all the animals that exceeded the size range of animal life during the Paleozoic (I.e. grew bigger than the largest eugeneodontids) were Amniotes.
There are a few notable exceptions, namely whale sharks, megatooth sharks, and pachycormids (esp.
Leedsichthys), but they are remarkably few and themselves constrained to a few specific groups. So it seems there are (probably complex and multiple) factors favouring amniotes when it comes to giant size (probably to do with respiration, circulation, skeletal structure, and certain ecological adaptations, such as terrestrial herbivory, among others).
More broadly, all the exceptions are also vertebrates; no documented invertebrate has ever reached a size that even comes close to any of them (although it’s possible there were some extinct cephalopods that we have little or no record of that might have grown larger than we give them credit for). That invertebrates are unable to match the size of the largest vertebrates likely comes as a surprise to exactly no one, as it’s easily explained by major physiological constraints (such as of the respiratory and circulatory and, of course, the skeletal system).
So of course in a time before the evolution of the first amniotes, and during the early evolution of vertebrates in general (which also started out very small, and don’t seem to have had an early burst in terms of large body size, unlike some of their subgroups, such as ichthyosaurs and cetaceans later on), animals overall can be expected to have not reached comparable sizes to later on. And during the early evolution of Amniotes, it is intuitive that it took them some time (and the aid of a major mass extinction) to radiate into their full range of potential ecologies and environments (e.g. secondarily aquatic amniotes include many of the largest animals ever, but they were only just starting out as small, semi-aquatic forms in the Permian), thereby not evolving their full spectrum of potential sizes yet.
If there had been some major innovation among invertebrates or non-amniote vertebrates allowing them to break free of their constraints and reach much greater sizes then, it would throw up the question as to why that innovation went extinct or at least wasn’t passed on to any extant lineages, and why we even have our vertebrate-dominated megafauna today. So that would suggest invertebrates likely were bound by the same size "ceiling" they still have nowadays, while vertebrates simply hadn’t "fully come into their own" yet.
For example, I don’t think arthropods back then had any major anatomical or physiological features that allowed them to grow bigger in the Paleozoic than they could grow to today (I could easily see a modern crustacean reaching the size of large eurypterids if there were no external factors preventing it, heck, lobsters do reach sizes matching many mid-sized eurypterids even now), the reasons they grew bigger were likely environmental and ecological in nature. Higher oxygen concentration has been commonly cited for terrestrial arthropods (therefore relaxing the limits of their inefficient respiratory and circulatory systems), but lack of competition or predation pressure from vertebrates was likely at least as important. The reason Eurypterids didn’t grow to 5 or 10 m long is likely that no arthropod with standard arthropod features could–this is one of the rare cases where I think it is warranted to speak of substantiated "hard size limits", as only they can explain why invertebrates throughout the evolution of life have never been able to grow much larger than they do today. And had arthropods (or cephalopods) evolved features to break free of these constraints, then maybe we’d all be arthropods (or cephalopods) now, and the amniote radiation may never have happened.
So the key is to determine if it is internal or external evolutionary constraints that are holding back the evolution of greater body sizes in a particular taxon and at a particular point in time. In the case of Arthropods, it was probably internal ones in the Paleozoic (and mainly external ones now, at least for marine ones), but for vertebrates, we know that they could reach much greater sizes, without the help of any more favorable environmental features that could have relaxed some sort of internal constraint, so likely the reason they didn’t get as large in the palaeozoic mainly has to do with the lack of ecological benefits or resources to do so.
But two caveats:
1) While the largest animals of the palaeozoic don’t reach comparable sizes to the largest Mesozoic and Cenozoic forms, and there’s a case to be made that the average sizes of animals overall were also smaller (although I’ve made no attempt to quantitatively confirm this), once we look within specific groups or categories of organisms, this trend falls apart. There were some of the largest ever freshwater fish and non-tetrapod Sarcopterygians (such as
Rhizodus), some of the largest amphibians (
Mastodonsaurus is Triassic, but
Prionosuchus is also a strong contender, and it’s Permian), and of course without a doubt the largest arthropods (numerous giant eurypterids and
Arthropleura).
What these groups have in common is that they all had major diversification events and periods of ecological dominance early on in the Palaeozoic, but were largely replaced in these niches later on (of course arthropods are probably more diverse than ever, but they are almost universally small, whereas eurypterids or
Arthropleura filled niches of large aquatic predators and large terrestrial herbivores respectively, before there were vertebrates that took over these niches and that were less subject to size constraints due to their bauplan and physiology).
So the Paleozoic may not have been a time when animals overall grew very large, but of course many animal groups still seem to have been able to hit their respective size maxima within that era one way or another, it’s just that the groups with notably higher size maxima than the one in the Paleozoic (i.e. Amniotes, Selachians, Pachycormids) were either not around, or were only just starting out in the end of the Paleozoic.
2) As we see from the striking recent examples of
Lisowicia and
Perucetus, a new organism that completely overturns our understanding of the size evolution in a certain group or period can turn up seemingly out of nowhere. Until a month ago, we would have thought that animals in the Paleogene never matched the size of the largest Neogene forms, but that has now changed completely. Until a decade ago, we would have thought that non-mammalian synapsids never grew beyond 1 or maybe 2 tons in body mass, and that Triassic synapsids never reached sizes comparable to large coeval archosaurs. While it is unlikely we will see a change to the overall trend that throughout the Paleozoic animals generally tended to achieved smaller body sizes, it is totally possible that tomorrow someone could describe a new fossil apparently representing a total outlier to that trend (although as with any such discovery, some scrutiny when it comes to the size estimate is always advisable), for example a large whale sized eugeneodontid (as some fanboys on the internet have proposed before, based on very faulty size calculations for
Parahelicoprion) or some elephant-sized (like
Lisowicia) basal synapsid or parareptiles.
PS: one thing that’s probably not true is the claim that Carboniferous insects reached far greater maximum sizes than modern ones:
lamareauxtetrapodes.wordpress.com/2020/10/12/yesterdays-giants-life-and-death-of-giant-insects-part-1-2/It appears that there are no complete
Meganeura/
Meganeuropsis fossils that lend themselves to size estimation, but what there is may not be indicative of the commonly assumed 200-300 g body masses. The extreme size reached by
Arthropleura is beyond doubt though.
