Money Market Funds are SIPC-insured, which is largely the same as FDIC insurance, except you need to make a claim for SIPC protection whereas FDIC is automatic.

The main other difference as you mentioned is that they're not guaranteed to have any particular return, and they could go negative by breaking the buck, but that has happened exactly twice ever and after the second time, we got new regulations to further reduce risk. Current MM funds are probably more secure than traditional banking, at least in terms of how likely you are to have to deal with the insurance (i.e. a money market fund failing is very rare, and MMFs are often owned by investors instead of a bank or brokerage).