To be clear - at least in PADI - you are NOT an "active DM" if you DON'T have insurance. It's not a matter of "should."
True. There are 3 things required for you to be "active" with PADI as a DM. (1) Must successfully complete a DM program, (2) must be current on annual dues and (3) must have current liability insurance. The first is required to even get your PADI #. Items 2 and 3 are required to stay current. If either of them are not current, you are listed as Not in Teaching Status via their ProCheck website. This is for the US. There are different rules in each foreign country as far as whether or not liability insurance is required.