Ok, I googled around on this and the reason why people "outgrow" the more affordable VPS offerings seems to be because of the size of the database. The size of the database grows as more and more posts get stored in the database. That's why some forums have old thread pruning policies. How many threads over a couple of years old do you think people actually look at and read again? I suspect its very small. Therefore archiving very old threads may be a plan.
I don't think this site gets too much traffic to be problematic if the number of new posts per day is any indication. However I notice nginx is preferred over Apache and Postgres over Mysql for heavy traffic loaidng. Also gzip compression on page loading.
Sometimes its better to do a bit of performance tuning before running off to sign up for an expensive hosting plan.
Not really much I can say here. You could take this up with Jeff. I just know the history and I know that nobody involved here actually makes any money off of the site. I remember at one point Jeff was renting some server space and bandwidth out to some businesses (I think, if I remember correctly at least) to help offset the cost of the hosting, so perhaps that's part of it as well. We've had significant page loading issues in the past running on traditional plans that have worked pretty well for me on other forums I've run in the past. Being a fairly well known Christian forum, we do get a ton of bot traffic and we get attacked pretty consistently. The database is a pretty significant size, but I don't believe it is beyond any performance thresholds.
Anyway, I probably just don't have the answers you are looking for.