I use a single wheel drive Kettwiesel in county Durham, which has a few hills! The limiting factor is front wheel weight rather than rear grip. Too steep and the front hops sideways on every stroke.
Some examples from my usage may clarify. The trike had 2" Big apples on all wheels rear at 70psi, front at 55psi. The trike routinely has a Streamer faring fitted adding a little weight to the front wheel. The seat is fully reclined, reducing front weight.
On a bottom gear of 15" with no weight on the front wheel on a well surfaced dry road 16% gradient sees the front wheel trying to go left and some counter steering is needed.
The same conditions, but 20% gradient the front is going sideways by a lot, smooth pedaling may well get you up, but mash the pedals and you'll come to a stop. Add two lo-rider panniers to the front wheel rack with a couple of kilograms of stuff in them and it will sail up the hill.
Rough surfaces, loose surfaces or wet surfaces can all cause the front wheel to hop/slide over to the left.
The good news is if you stop it's easy to get off, pick up the front wheel and walk up the steepest part of the hill. I do this very rarely but compared to trying to push a tadpole trike which has run out of traction, dragging the kett' is a breeze.
I've had my Kett since 2008 and have had to walk a hill three or four times in many thousands of miles. Each time it was a loose surface that meant the front wheel could not be counter steered into going up rather than sideways.
Would I retro fit a differential? No, the very odd time when the trike has failed to get up a hill is not worth the substantial outlay on a dif'.
