You wouldn't want the Sponsorblock to be part of the download process, but rather the player. Being crowdsourced, it's not immediate and often gets improved/corrected over time, so a video's least likely to have good Sponsorblock timestamps right after being uploaded (when an automated program would likely be downloading it).
We need a Plex/Jellyfin/etc. metadata provider with the Sponsorblock info included. Could keep the data up to date, even after the videos are downloaded.
I don't know how common they are anymore, as Plex has moved toward hosting their own metadata and I've never bothered using any myself, but there historically have been some number of YT metadata agents (e.g., this one) folks could add onto their Plex server and pull the metadata from YT directly. Expanding something like this to also query the Sponsorblock API seems like it wouldn't be terribly difficult.
The harder part would be getting the player to incorporate Sponsorblock to actually use that data to skip the segments. Plex, in particular, seems unlikely to ever try something like this, as their business model is moving more and more toward ad-supported streaming content rather than improving the self-hosted media server that got them popular.
It does seem unlikely Plex would include this ever. Hate their generic pivot to ad supported bs. But as a lifetime sub to Plex I’m riding it down.
I hear jellyfin supports plugins which is one step easier.
At home I watch on an Apple TV with a nas running isponsorblock. Works well but is a single device/location solution. And I am still paying for YouTube premium.
For things I don't care enough to archive to my own collection, I use a Shield TV with SmartTube, an alternative client that blocks ads, incorporates SponsorBlock, and a few other nice tweaks. Definitely my favorite YT experience of all the ones I've tried.