Should I reconfigure my shared neutral breakers to have tied handles
If... you ever decide to replace an outlet, and you turn off the breaker that controls that outlet, and you remove the white &amp; black wires from that outlet... but the other paired breaker is not turned off, and whatever that breaker powers is drawing power... then the white wire in your hand is going to be live, and it will flat plumb shock you. Even with your breaker turned off.

If anyone else for any reason replaces an outlet and "does everything right" by turning off the breaker first, then they will get the blazes shocked out of them by that white neutral wire. That "anyone else" may be your best friend, or may be the next owner of the house who's got a pacemaker to keep their heart going. Your complacency here could result in someone's death.

It's not like anyone's suggesting a project costing many thousands of dollars or requiring months of work. A two-pole breaker costs about $10US and takes about five minutes to replace. If you need to shuffle all the wires around that breaker box, the whole job may take you two hours.

It's worth doing.