I don't think it's a bad of a solution to keep the studio separate.
We run several large-ish Sanity-powered sites at my work (none tied to our 11ty sites unfortunately), but we do keep the studio separate (or as part of a monorepo that deploys separately).
I'll probably pull existing Sanity data into an 11ty site as part of some project sooner or later and I think the separation will probably be a benefit, but I'd love to hear about any experience with any Sanity/11ty setup.