Beyond this, you can make shorter lived JWTs just fine in the browser and have the agents self-update. If you use Azure Entra or a number of other providers it works this way in practice... you keep your JWTs relatively short lived (5-15m) and can even check for jti revokation.
JWTs are incredibly useful for separating/reusing an access authority from your applications/api systems. You shift the attack surface and do it in a way that can be trusted. We use PPK for lots of things, including SSH all over the world. No, I wouldn't use shared secrets and I wouldn't use long lived tokens... but short lived, ppk signed tokens from verified/known sources are generally fine.
For that matter, it's often API keys that are really problematic. Just had to implement them... for me, the API key presents as a Bearer token as well, but there's a short "sak." prefix then an identity part (base64url uuid bytes) followed by a secret as base64url bytes... in the database is the uuid and a passphrase level salt+hash from the secret.. so the api key generated should be treated as a secret and is one-way to the database, so a db breach doesn't breach auth.
Even then, an API key leak is far mroe likely than a problem with a well implemented JWT solution.