I expect something similar to how Bitcoin is used: some people let Bitcoin Core download the full blockchain, but the majority uses light wallets that rely on a centralized server. Or multiple centralized servers, such as Electrum is using.
When a decentralized forum gets too big, we'll end up with centralized servers again.
There's not a whole lot of incentive to do so, and you're right except I think it'll just be a select few which would host the servers, which is centralised to a point anyway. I guess you could argue that 4/5 users hosting the servers is better than one central figure, but Bitcoin works because there's a common interest in hosting nodes, and it's beneficial to a currency they use.
Most users aren't concerned about the integrity of the forum, at least because they don't think it's being maliciously altered in the first place. So, the motivation or incentive is much lower.