Looks like there are two issues here that don't HAVE to be tied together: (1) Pausing the game to insta-heal and (2) having the Pip Boy pause time.
I think everyone can agree that pausing the game to instantly heal is at least potentially game/balance breaking. Easy solutions are to make it so that you cannot pause the game (but then you could presumably hotkey sitmpacks and just jam that button over and over) or the more sensible solution, to have stimpacks heal ~over time~ as they do in the hardcoe mode of New Vegas. And not "stack", so that you could only have one stimpack's over-time healing effect on you. Another extreme solution would be to give stimpacks weight, to simply limit how many you could carry. Frankly, having ZERO weight always seemed a little immersion-breaking (of course injecting something that can miraculously heal bullet wounds is also a bit of a logical stretch). That said, I don't want two pound stimpacks, but 0.1 lb stimpacks would let me carry 20 at just two pounds of encumbrance and I could live with that.
The other issue that gets tied in to the insta-heal stimpack "problem" is having the Pip Boy pause time. Thing is, this should not be a consideration in the same debate since you could just hotkey stimpacks and still insta-heal without pausing time so penalizing the pip-boy's ability to pause time seems unnecessarily harsh. Pausing the pip boy is desirable NOT for the ability to heal, but so you can look at your inventory, read a quest objective, scan a quest note you just picked up, or check your map, etc. Having to do that while the game world moves on around you could potentially be hazardous to your health as enemies start peppering you with bullets while you're checking a note.
Yes, it's more "realistic" that if you had your nose buried in a map you would not see the bad guy sneaking up to slam a sledgehammer on your head, but at some point gameplay has to trump realism.
In any event, I would be happy if the Pip Boy stopped time entirely AND stimpacks had very very low weight AND healed over time AND could only be applied one at a time. That looks like it would solve most issues.