I don't think you need to be that good at Go to recognize that. At least at the 1-dan level, I can say that looking at a 17x17 board, I can feel that the strategy would be quite different and the center influence would be worth much much less. I wouldn't want to play on it- it feels cramped, like a whole dimension of the game has been sharply reduced.* I don't feel the same way about 21x21 and would be interested in playing on it, but perhaps that's natural because 21x21 must be more complex than 19x19, even if it's not as balanced between center and edges. I might also just be somewhat biased due to liking to use central influence.
*It's true that skill (among humans) on 17x17 would probably be very similar to skill on 19x19, because 90%+ of skill in Go is tactical fighting skill. Or rather, it's a limiting factor. If you have the greatest strategic play in the world but the fighting skill of a 5k, your rank will be something like 3k. On the other hand, you could know nothing about opening theory and it probably wouldn't hurt you more than 1 or 2 ranks- because your opening or strategic play would have to be amazingly bad to be worse than just letting your opponent play 2 handicap stones. But the strategy is probably where the majority of the fun and creativity comes from, so it's painful to lose it.
Is 8x8 Go actually harder than 8x8 Chess, though?
Chess can loop game states much more than Go can. The entire set of possible moves in Go for an 8x8 board is like...about (64!) assuming people don't place a piece in the same square more than once.
Hmm...yeah, ok, so that's roughly 64^64 = 2^(6*64) = 2^(384). Haha, ok, yeah, no, you're not searching the entire decision tree by brute force.
I believe 7x7 Go has been solved. I don't know if 8x8 Go would be easier to solve than Chess, but computers could probably crush humans on it at least. 9x9 Go is already for humans much less "hard" a game than Chess, but that could be a consequence of how humans think.
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Congratulations to SuperNiceDog, Guru Winner, who was smart enough to pick
your 7 time champion, Link.