Space saving car parking - GIF

[Floradawg]

It doesn't look like it saves enough room for the complexity of the method.

[Karl_H]

It doesn't look like it saves enough room for the complexity of the method.

I agree.
Assuming that is 30º angle, it would save about 15 % of the length of the car, but would also save the fore and aft wiggle room needed to parallel park. The wiggle room probably saves more than the savings from lifting the front.
If the mechanism only had lateral movement without any elevation, there would still be some advantage, but with a lot less fuss.