"...the bore diameter is .224 for a 22 mag..." Yep. However, it's not a pressure issue. It's a bore diameter and chamber area dimension thing. Plus the cost. .22 mag ammo is considerably more expensive.
If you want a bit more punch than a regular .22lr, buy a box of each hyper-velocity .22's(Stingers, Yellow Jackets, et al) and see which brand shoots best out of your rifle.