You are indeed fortunate that the aides supplied/managed by the CCRC were excellent (not the case at my parents' CCRC) and that the CCRC was responsible if one called in sick, etc. Someone managing aides for an individual at home is on the spot if they get a call that the aide isn't coming into work for the next two days; the agency may or may not send a substitute.
But you said "when we decided" -- and that is key. You made decisions about levels of care, etc. The CCRC cannot/will not do that beyond calling you or calling for an ambulance. So the resident must have a "responsible person" (RP) on call.
Suppose your mother falls and breaks her hip (God fordbid). I'm curious: how does that scenario play out? Does the CCRC call you and say they're putting her in an ambulance to St Elsewhere Hospital, and the ball is now in your court? If you're not close to the hospital, does everything then transpire by phone between you and the hospital? Does the CCRC have any responsibility for / interest in her at the hospital?
Sadly in the case of the CCRC my parents were in, the resident was simply put in an ambulance, the RP was called, and the CCRC was then out of the loop. If the RP couldn't be reached right away, it was up to the hospital, not the CCRC, to continue trying. And meanwhile the elderly resident was there at the hospital, alone without an advocate.
For anyone researching a CCRC, outlining specific "what if" scenarios is key in understanding where responsibility ends and begins, and if the RP should be nearby (1 hour?) and available 24/7 by phone. We did not ask those questions when my parents went for their 9 months in a CCRC. I wish we had.