If they could up the premiums any further, they already would have.
Sure, the first execution may cause them to go into hiding and hire security, but if it happens a few more times they're gonna start rethinking their policies, for their own health.
If they did anything that would negatively effect profit they'd be removed by the Board and be subsequently unhirable. They'd have to martyr themselves for the proliteriat. They can't wisely invest into such sacrifice unless they've confidence in the prolitariat's ideological commitment.
We should all right now go to the leadership pages of all the major insurers. If there were a sudden spike in traffic on these pages it would be noticed. Nothing wrong with putting a little worry in their lives.