This is completely correct. We use--sort of--an app called Family Wall. It has a calendar and a message board. I use it all the time. BL uses it all the time. Guitarist sometimes. Drummer, as best I can tell, never. So we end up using fazebook messenger, which creates long and mostly pointless posts, except for the guitarist who refuses to use fazebook. Somehow, we get it all done. It ain't no damn silver bullet, that's for sure.
The problem is that this is one of the areas where people pull out the "it's just a hobby" card to excuse not doing what they're asked to do. And in this case, I agree with them, and because I am who I am I'd rather let you know up front that it's not going to happen, because I don't care about losing out on your job over this minor thing. If this is what is important to you as a BL then our priorities are not aligned.
The world is not going to end if it takes a minute to get in touch with everyone through a group text to confirm availability and, as some have mentioned, you pretty much have to do that anyway because people won't do this reliably. The people booking your hobby band into hobby venues are canvassing and they are not sitting there by the phone to wait for your answer before they can do anything else. They are offering you one date, then offering the next band the next date, and when you get back to them they'll either confirm what they offered you if you are available or ask someone else. Immediate response time is not that critical, they know there are plenty of bands who can book that date if you can't and they won't be in a bind if it takes you a day to come back and say no.
The point about knowing if someone isn't available is a stroke of luck that only means you're going to need to find an alternate date and start the process again. It's helpful, for sure, but it doesn't save you the chore of needing to contact everyone else at some point.
At a higher level you might need a manager who can speak on the band's behalf, but at that level you're also going to be expected to make the band a priority, just like any job. So if someone calls with a big money gig in Tahoe and your manager wants you to do it, that gig is going to get booked and whatever plans you had that week are going to change. Important, unyielding things, like your own wedding, your daughter's wedding, etc. should get calendared on the band calendar, but otherwise you'll be expected to take your vacations when the band is not active or touring. If something happens to you where you absolutely can't make it you'll likely be replaced, either with a sub or permanently.