This seems a bit like a solution in search of a use case. There are simpler solutions for this particular usecase. Let's take an extreme case: You have 250 million paying customers you want to cache access to. Yeah, that's way more than you probably have, but the point is that you can keep 250 million integers in memory no problem what so ever. It fits in a gigabyte. There are raspberry pis with eight times that amou…
Obviously you don't need bloom filters if lookups are cheap, but you're ignoring all of the cases where lookups aren't cheap. You can't always put the entire database of everything in memory. Consider cases where the check is done client-side and requires a network request. A bloom filter could allow you to optimize away a network request in some, though not all, cases.
In general, bloom filters are mainly useful for the sort of data where lookups are cheap, that is, testing for membership of a set, and that is typically one of the operations a database does really well.
In most cases where you just want to save a network roundtrip, a LRU cache is often a lot easier to get right and is much easier to keep consistent against mutable data.