Requests are not equally probable, they'll follow some sort of power law distribution. Caching will work well enough in that situation: common queries will remain hot and rare queries will fall out of the cache. The net effect is faster.

SQL databases often have query caches for this reason.

I agree about DoS, but I figure that's going to require the usual defences around throttling. Ideally in the database, but most databases of any kind don't have workload partitioning.