Like you said, hard to compare apples-apples without more info but couple 1000 users with 100s of writes/user/day sounds like it would handle fine on a $1/month vps (we have far higher workloads running few $1/mo, if I understand you correctly).
Not saying that you should spend time on that; it's probably insignificant on the p&l, however, other people should know there are alternatives still and aws is not always, automatically, the right choice (in my mind, it almost never is actually).
How is that different from managing aws? Because in my experience (of 20+ years) there isn't any for most projects. There are reasons to pick aws, but, for most of them, this is not one of them.
I guess it depends on what AWS services you're using and how complex is your usage. If you're only using Dynamo you shouldn't need that much management, or if you're using Fauna you need zero management.