My personal experience with this. It obviously isn't that big of a deal to lose a tire. When I worked at MesaAir, I was parking a CRJ200 and I notice the #1 main tire was shredded. After all the pax's got off I told the Capt about it and he walked over looked at it and told me basically that he knew about it on take-off but since no warnings had gone off he continued the flight to PHX. So tire burst on takeoff, flew the flight, and then landed on 3 mains. No big deal. Plane ended up going to maintenance with a damaged flap section that had to be replaced, probably a new wheel and tire, and some other minor cosmetic fixes. CRJ is a tough bird.
Losing a tire and losing a wheel are two entirely different things. It also depends on what else is down there.
A number of years ago, Santa Fe tower noticed a C-310 wheel (not just the tire) come off about the time of lift-off. They bellied it in at ABQ.
I'd sure not want to face the landing gear stub dig in (even on concrete) without something on there to roll.