I had the same thought initially, but the problem I see is that breaking several keys in the same keyspace shares work. e.g. if you want to invert a one-way fun

I had the same thought initially, but the problem I see is that breaking several keys in the same keyspace shares work. e.g. if you want to invert a one-way function, that's a tough problem. But if it's a 10-bit function, you can just create a full table by brute force.