Most paid forums will keep the code updated
Most likely, yes.
Although, they're also pushed to add a lot of functionality all the time, but technologically speaking, they're probably over five years ahead of the free players, minus NodeBB / Discourse, as they offer the software for free there, but have an official paid hosting service.
Those two are probably more modern than the paid players. Still, it's not like they're doing it for free, they have a service to pay the bills.
I think this is more to do with the fact that many people have just lost the passion for forums and generally developing forums. Also, with more advanced new players, there isn't much enthusiasm for modernising older systems.
The main problem with the more modern players, of course, is that their interfaces are alien to anyone who has ever used a forum. If you look at the commit history of new players, they're extraordinarily active, while some major players are nearly dead in the water.
That's not a free software is bad. That's lack of interest. Disinterested developers.