A sure grip would not like different tire sizes. A few 10's of an inch may be OK but not too much... that's why it important to match rear diameter pretty close.

Also, on the spare question... I always have and have recently used a full size spare for my DD Durango. Piece of metal on the road kicked up by the front tire and perfectly positioned to poke a 1/2" hole in the nice Michelin rear. Glad I could change the tire and continue my road trip. My wife somehow picked up a 3/8" x 7/16" combination wrench in her rear tire on the way to the gym. In through the tread and poking out the sidewall. I keep it as a souvenir. I was glad to get her back on the road with a quick tire change. My older daughter carries a full size and my younger daughter carries a full size + donut. Both have used theirs more than once. On the Neon they both drove at different times they have managed to take out several wheels as well as tires... and get home with no assistance with a quick tire change. All that is why I like to have a spare!