There have definitely been some core "groups" that generally started and stopped about the same time, and I would argue made some of the better seasons of SNL... late 70s, mid-80s, mid-90s, and late 2000s... but there is a larger cast it seems lately, with changes, so it does feel less consistent.
I think also SNL faces an insane amount of streaming/alternate pressures that no longer makes it a weekly staple of entertainment that some used to rely on it for.
That being said, I watched a little bit of it last weekend for the first time in probably 10 years. Ironic.