That is, at what point do you stop buying complete ARs and instead buy uppers to swap back and forth? If you have a pistol, carbine and rifle lower, do you accomplish anything by buying another complete rifle/carbine rather than an upper?
Sort of depends on the optics you are using. If you go straight iron sights swap as often as you please. If you are using precision scopes try to keep the weapon whole. While not a major issue, even moderate wear and tear will change the seating over time...
How many is enough for what? I have a lot of blank wall space. How many to fully occupy as much gun wall as I can create? 300+. How many to fill my safe? 40+. How many to fill all space I'd be willing to fill if there were no other obstacles? Thousands. How many can I shoot at once? Well, if I practiced it, perhaps 2 but mostly just 1. How many to fulfill my interest for fun and for the enjoyment of building them myself? Probably several dozen. How many to own to grandfather in case a future ban allows grandfathering? 50? 100? It's like get all you might ever want because you may never get another.
For lowers, it depends on what type stock you need. A pistol upper won't do well with a rifle stock lower. Then choose M4 stock, A2, thumbhole, folding, etc and the buffer tube(s) to fit for the lower. So, at least 3 lowers to fit your mix and match uppers, and legal stuff for pistol stocks/lowers.
For me two lowers and three uppers. One lower has a 2 pound trigger and is mated to a heavy barrel upper with a scope. The other lower is used with two low cost uppers, one with a carry handle and iron sights, the other a flat top with a red dot sight. That is all I need.
I don’t swap uppers because when I need a gun I need it now. At the moment two seems adequate but I’m considering setting up one of the two “spares” I have as a clone of one of my current rifles. My two current AR’s are an old 20” heavy barreled Bushmaster with a YHM chromoly suppressor and 3-9 glass. Dang thing is great for prairie dogs or calling coyotes/fox but you don’t want to carry it around all day. So my second AR is a Colt 6720 pencil barrel with a titanium Gemtec suppressor and an Eotech exps3-0 holographic sight. It’s light enough to drag around between the tractors and pickup etc. Both have aftermarket triggers but are otherwise stock. My reason for wanting to clone the 6720 is the law prohibiting a chambered rifle on public roads. Some days if I want to be legal I have to either stay unchambered on my home property or clear the rifle numerous times to travel to a different field or pasture. With two rifles set up the same I could leave one chambered at home and have an unchambered rifle for the pickup and trucks. At one time I was set on an SBR or braced pistol, but have decided a 16” pencil barrel with titanium can is light enough and I’m not giving up muzzle velocity like I would in a shorter barrel. Oh, everything is in 5.56 for me so no reason for extra uppers there either. If I had gone to an SBR I would have gone 6.8 SPC. I guess the short answer to your question is it depends on if you need every configuration ready to shoot at all times or not.