The point of allowing and supporting integer komi is to allow draws as a possible common outcome in the game. Since the typical practice is to avoid draws with non-integer komi, this does change the game in a major way, perhaps quite unfamiliar for many go players (myself included). Instead of (nearly) always having a decisive winner (even if having to be decided by the thinnest of margins), the possibility of draws allows for a third outcome that indicates that neither side was able to decisively outplay the other.
I think the difference in mentality between requiring a decisive winner vs allowing draws can also be seen when comparing some popular worldwide sports like soccer and chess (where draws are very common) vs the popular sports in the USA (i.e., American football, baseball, basketball, hockey, where draws are made at least quite rare to virtually non-existent).
In games where draws are possible, ideally we can hope that wins are earned by decisively and significantly outplaying your opponent, rather than just winning by default (since someone has to) for just slightly edging them out.
However, integer komi go still does have a pretty thin margin covering the possibility for a draw. Another interesting variation would be to consider go where a player has to win by a margin of X points (after factoring in komi), otherwise the game is declared a draw.