Mapped memory is part of that lying. If you want to use efficient mmap of huge files without lots of manual bookkeeping, you don't want the system to actually allocate as much memory as you specify. With overcommit off you're setting aside memory you're almost never going to use.
Many databases rely on the overcommit being possible.
Partially. Without overcommit the system needs to guarantee you have enough backing memory to allow you changing the whole file before the drive writes back anything.
Many databases rely on the overcommit being possible.