For me, switching between the two grips is not a problem. The “rhythm” grip has been my default since youth, so it’s not something I have to think about. It’s the pad-to-pad grip which took getting used to. It is unquestionably faster and smoother.
As it happens, the pick orientation is pretty much the same for both. The pad-to-pad grip is just faster, hands down. (The wrist orientation is a little different for each.) It’s a ‘trailing edge’ approach and that’s faster for me. Conversely, the conventional grip is ‘leading edge’ and that provides a bit more definition when riffing. For funk strumming, the pad-to-pad grip doesn’t feel right to me.
The conventional grip is better for things with lots of downstrokes (such as blues riffs or popular melodies with quarter notes) because it provides more definition. The pad-to-pad is better for smooth speed.
It was not a choice I made but a habit I discovered. (I use Jazz IIIs and had no idea I was an upward pick slanter for a long time because when I look down at my hand, I just see the thumb, not the pick! ;o) With the pad-to-pad grip I see the whole pick.
I can play rhythm that way too. But I often play the other way. (It’s not something I decide to do; rather, when playing and taking a glance at my hand I can see that is what I have been doing.)
If something is a problem and can only be played (by me) one way, then I have to play it that way.
But most things that aren’t real fast I can play both ways.