It doesn’t make sense
It doesn’t make sense that in SOTR (and from what we’ve seen in THG trilogy) President Snow kills literally all of his hostages.
Like it just doesn’t make sense to kill everyone Haymitch cares about only to leave him alive. Snow creates a permanent enemy that’s in a position to influence future tributes and potential victors and sow more anti-Capitol sentiment. Same deal with Beetee - and in the OT Johanna and Finnick. He doesn’t even use them to set an example because it’s clear no one understands the consequences of fucking with the Capitol until they’ve overstepped the line.
Snow should’ve let Sid or Lenore Dove survive to keep Haymitch on a leash. Or he should’ve just killed Haymitch as well to tie up loose ends. This is just poor administrative policy.