All go handicapping systems eventually stabilize so that there is a rough transitive relationship between anyone whose rank is stabilized. The traditional free stone for B handicap system works pretty well up to 6 stones after which it starts to break down.
The key thing about handicapping systems is to assign a meaning to one rank grade. So the default meaning of "one free stone" could be changed to something else.
If the something else is a very small change, such as "1 extra point komi" then the winning percentage of someone who is better, without this komi will be low. For example if you played with a system where every stone in difference in strength would be compensated by just one point in komi, then a 4d and a 1d would actually be very close in strength - and a game played even without handicap would not be weighed very heavily at all in the 4d's favor.
On the other hand if each handi stone had a bigger advantage, then playing unhandicapped games between ranks would be really tough, and there'd be tons of variation within one rank.
To make them easier to understand, alternate handicapping systems could be designed so that the size of one rank difference corresponds to the official one, but this is not a mathematical necessity.
That said there are lots of ways to handicap things that would be just as internally consistent as stone handis, and some of them might be more fun. In the end people might have different ranks in different handicapping schemes.
Games are played with 10s fischer time and for every stone difference, the weaker player gets an extra 3s fischer.
Even game, but B gets free points. People haven't played with this very much, but theoretically one normal handi stone is worth about 15 points. So instead of 2 handis, just play even and give B 30 points extra. I think this would produce interesting games... but it might force people to spend too much time counting.
It is actually kind of weird to call "2 handicap" that, because in that game, B actually only has one free move, and additionally, unlike a normal game, he is required to put his two stones in the opposite corners. With "3 handis" he gets 2 free moves. The reason for this is that the "first" handi stone is actually the removal of komi. So 0 handi == B plays first, w gets 6.5 komi. 1 handi == B plays first, 0.5 komi. 2 hand == B plays 1 free move, plays first, and 0.5 komi.
There are lots of unwieldy ways W could be handicapped