Oscar, as I actually wrote, the maximum size ever confirmed for a wels were 2,78 m and 144kg. And you should really not believe in every old report only because you would like it if it were true. You won´t find photos of any bigger specimens. The specimens on the photos are actually much smaller than you think, about in th 2,2-2,3m range but look much bigger cause of the forced perspective.
The fish on the old photo is without any doubt a beluga and not a wels, this is for sure. It is also false to think everything was bigger in the past. Okay, many fish are today actually overfished today and there are often smaller average sizes and lesser big individuals. But in the case of the wels it is nearly the opposite. During the last twenty years there were much more reports of exceptionally large specimens than in than around 1900. This is not only because there is today much lesser inland fishery in Europe than in earlier times, but also because this species was introduced in many other regions like Italy or Spain. They have there much better conditions than they had ever in their natural habitat, because the climate is much better. Similar to many other examples, they grow much better in this new regions than in their original habitat.
A highly interesting thing is that even in old books there is no indication that this species was ever bigger. I own several old reprints (1923) of a series about the wolrd´s wildlife, by Alfred Brehm(1829-1884)which was one of the most famous german zoologists of all times. In the book about fish, reptiles and amphibians he wrote about Silurus glanis, that according to Heckel and Kner specimens of 3m and 200-250 kg were not rare in the river Danube. Okay, this alone is strange, because a wels of this lenght would be much lighter. Even the 2,78m italian specimen, which was very fat, weighed only 144kg. Even if you keep in mind that the weigth increases with the cube, this seems ways too much. The wels seems to grow fatter in warmer waters, for example in italy to southern France, and the specimens from Germany for example, have often a lesser weight than same-sized specimens from Italy or Spain. The Danube is not especially warm, so I really have problems to accept this claims. It seems that there were also authors which wrote further information in this issue, because there is a specimen mentioned, which was caught in 1894 with a harpoon, and which was unusual large. But even this one, a specimen which was already in the 19th century (when you could still find very large sturgeons in the river Danube, and when there was much lesser population than today) a sensation, was only 2,2m and weighed 68kg. For a middle-european wels this is very large. But if the wels could really reach a weight of more than 200kg, isn´t is a bit strange that already 2,2m was quite unusual even in the late 19th century? Furthermore even those old authors don´t speak about 4,5m or 5m lengths. Interestingly today there are some even larger ones known, like the one with 2,47m. The even larger ones from Italy show that this species has the biological potential to reach sizes of close to 3m (and note, 3m are not always 300cm, but very probably also sometimes lesser...) and as the amount of available food is also a very important factor for the growth of this species, I could imagine that in the unpolluted big rivers and lakes with large amounts of baitfish, in some exceptional cases some specimens probably reached even in the native habitat lengths close to 3m, but this was surely never average.
I would also don´t give too much about all the reports of alleged giant flatheads and bluehead catfish. There are countless stories of specimens allegedly the size of great white sharks or even cars, and nearly everyone seems to know somebody which has an uncle or a friend which has seen one. Okay, if they would get that big, why was there never an actual proof for this? We would have countless confirmed specimens well over two metres, but in fact there is not a single one. You have always to keep in mind biological limits. In a population you will find a lot of specimens with average size, a lesser part which are big, a small part which is very big and a very very small part which is unusual big, it´s the same thing with fish as well as humans. To take again the wels as example. 2m is already a very rare and big size, 2,5m is extremely rare and extremely big and the record of 2,78m is like a lottery win, one among many millions. Perhaps sizes around 3m could be able, but everything even bigger is just unrealistic.