I have some thoughts for you as someone who's done this before. I used to run a file hosting site called MediaCrush with a buddy of mine. It was moderately successful, but we ended up shutting it down. I later switched to a file host called pomf.se, which eventually was shut down as well. I wrote a blog post that sums up my thoughts on public file hosting: On the profitability of image hosting websites - https://drew…
There are tons of pomf.se clones - many that have been going on for years as well. The important part for many of these hosts is that (a) enough people donate to keep it online and/or (b) the community remains small enough to remain affordable for the dev. Personally I use a combination of safe.moe and mixtape.moe.
Often times I've noticed these are "labor of love" projects where a dev can work on learning how to (a) keep a server running and (b) upgrade services without any/significant downtime, etc. Standard DevOps things. The monthly cost to these sort of people is seen as a "learning cost" in a real environment where they have hundreds of, if not thousands or more, users depending on them to not mess things up.
>I hate that if I look at a forum post written >5 years ago, odds are all of the images will be broken.
Inactivity pruning is largely to blame for this, not just new websites going under. IIRC, even Imgur does pruning after 6 months of inactivity (no views) which is totally possible on niche technical forum posts.