Who did Kirk inherit from Pike's crew

I could well believe in a curse. But it must be one that nobody in-universe believes in, or else either Starfleet or Kirk would take it into account somehow. Starfleet never assigns Kirk to these hair-rising adventures with terrors from the deep - Kirk always stumbles onto them on his own, or then is the random closest skipper to the spot where Starfleet needs to vector somebody. And Kirk never ever comments that his lot would be a special one in carrying the burden of defending mankind or Federationkind from said menaces.

Then again, the ship may be but a shell. Pike commands 200 people, Kirk 400-500. Perhaps the ship when configured to do milk runs to Rigel is a worthy command for a Lieutenant Commander (with a bright Lieutenant doing in a cinch), while the same ship when configured to explore beyond the known calls for a Captain (with a bright Commander doing in a cinch)?

Ships being routinely reconfigured for major changes in crew strength and mission are a new phenomenon ITRW, and none really undergo 100+% changes in crew numbers... What we see between the two pilot episodes is more like a 1800s conversion of a humble collier into an ocean-hopping ship of exploration, with the packing onboard of countless specialists, noblemen dilettantes, and their high-ranking warden.

Whether the comparison is apt can be debated with new evidence when DSC S2 establishes whether NCC-1701 under Pike and in the 2250s was a decrepit relic that was reinvigorated for frontier duty in the following decade, or an old warhorse still going strong and representing the cream of the cream. DSC S1 already depicted the ship type as a good career move for those hoping to make good quickly, but perhaps because it was "easy" for being so decrepit and insignificant?

Timo Saloniemi