S3 storage is cheap. Like 2¢ per gigabyte per month.
At that rate, 5,000 users could each store 100 high-res images for ~$20/month all together. (10,000 users X 1MB X 100 images = 1,000,000 MB = 1,000 GB X $0.02/mo)
AWS hosting costs can add up quick, but -- unless you're storing HD video -- the bottleneck is probably not due to S3.
https://aws.amazon.com/s3/pricing
My guess is, the software and DB schema for the message boards weren't designed to support the sheer volume of posts that have accumulated over 20 years. If basic tasks, like retrieving posts, require complex queries across multiple tables, it can reach a tipping point where performance degrades exponentially. Simply throwing more hardware at it may not solve the problem.
I know there was a software upgrade a few years ago, but maybe that was just a temporary solution.