Servers in workplaces are often ephemeral. It's easy enough to write provisioning code that updates the system terminfo database, but it needs to be written, tested, reviewed, and deployed. Speaking of deploys, how are your Q1 OKRs shaping up?
That is what kitty's "custom SSH wrapper" does, if I understand correctly. Each time you ssh into a server, it will copy kitty's terminfo file if it doesn't already exist.