I'm fairly sure this suggestion has come up before, and there are problems with substituting either way.
Large Rifle primers are a few thousandths higher than Large Pistol. This can cause trouble in either a semiauto pistol or a revolver, as the difference is large enough that the LR primers can no longer be seated flush.
Large Rifle primer pockets are a few thousandths deeper than Large Pistol primer pockets. This can cause trouble with LP primers whether they are seated to the bottom or not. If seated to the bottom and properly "sensitized", the firing pin might not reach the primer. If seated flush, the firing pin may simply seat the primer deeper rather than firing it.
The rifle/pistol primer substitution is done occasionally, for small primers. Those have the same dimensions. There the concern is largely limited to pierced primers if you use pistol primers in a rifle cartridge, and possible ignition problems due to less firing pin force if you use rifle primers in a pistol cartridge.
IMO, while a lot of the hobby is about experimentation, there are some things that just don't work. Rather than substitute primers when the type I need is "gone", I would keep a reserve and re-order when stock on hand reaches an appropriate level...