Not necessarily. I have (as well as many other owners) 235/85-16's on stock rover rims and have NEVER lost a tire off the bead, even when aired down. I wouldn't put that tire on a 5" rim but seems to be fine on a 5.5" and 6" rim.
Last time I looked for a 7.50-16 I found that Pete's tire and oil in Webster could still get them for you. They aren't really obsolete, just not common anymore. That's why I personally wouldn't put that size on. A 235/85 you can get just about anywhere as is the case with any metric size tire.