Thats a great Idea!
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Go has no retrograde analysis, because any legal position can be reached in a trivial way: by having each side place their stones in the position one by one, and passing once theyâre all placed.
While the question for how Chess positions could have arisen is arbitrarily difficult, and thus more interesting, it also has a downside. Namely, that we cannot count the number of legal chess positions exactly.
While for Go, we know there are exactly 208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935 positions [1], for Chess we only know there are approximately 4.8 * 10^44 [2].
So in some sense, Go is better by 13x13 digits of precision:-)
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Although Go doesnât have the same strictness, you can still do retrograde analysis with the assumption the position was reached by players making sensible moves and not passing. Indeed this is often how I do a positional judgement of an early game position: not be statically counting territories or influence, but working out what sequence of moves lead to it and then thinking âthis sequence was a joseki / fair, but then this one looks like a mistakeâ and summing those mistake deltas.
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On the topic of unusual problems:
Black has just played but it was a mistake, as now white can kill. What was blackâs last move and what should he have done instead to live?
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Iâd assume black played at B2, while they should have played at D2.
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aka, tewari analysis
It depends a bit on how you define what a legal position is.
If you demand that the set of legal moves can be deduced from the position, then a superko rule would need positions to include history. With simple ko rules, you can have the same configuration of stones on the board, but for any ko, it should be part of the position whether it had been taken the previous move.
I can imagine very rudimentary retrograde puzzles possible, like the one shared by @Uberdude above, there the information that Black could have lived tells you what the last move is.
The number of captured stones can also be used to give more information on the history of the board: it can tell you whether a ko might be recapturable, whether one of the players passed more times than the other, whether some empty territory might be the result of a capture, etc.
Iâm sure some retrograde puzzles can be made with this.
White gets a ko after D2 B2, so I would have phrased the question âwhat should he have done instead to live conditionally?â
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Black played B1, capturing white stones at A1 and C1. If Black had played D2, White could not have prevented Black living with B1 the move afterwards, since the throw-in would have been suicide.
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Black could have lived with no ko, so as the question was phrased carefully, a hint that wasnât the answer 
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Correct!
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Ah, youâre right; Black could have lived unconditionally. Their last move was not B2. Nice retrograde problem!
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I prefer Go because its handicap system is more flexible. If youâre stronger at Go than I am, you can give me an appropriate number of stones, and we can have a game thatâs likely to be enjoyable for both of us. If you can give me âa pawn and a moveâ at chess (much less a piece), it changes the nature of the game substantially from the outset.
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I started playing chess a few weeks ago.
A few online friends and I occasionally play random fun games together, and that evening, we were just goofing around with Crazy Chicken Horse, Escapists 2, and then somehow ended up playing chess.
It was waaay past midnight, and we were (are) all pretty bad. (At least we knew the rules.)
Aaaand we had a lot of fun with it. We kind of got hooked â now we play more or less regularly and are improving step by step.
So right now, Iâd say chess is better than Go. Completely unbiased and objective, of course. 
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