Sadly I've had the same experience. I've had to rebuy a couple games on steam because the older gog version wasn't version compatible with my friend's clients. That really burned my bottom.
In fact the only time I recall a Linux-native game not working out of the box was when I got the game 'The Raven: Legacy of a Master Thief' on Steam, and that was due to some wonky configuration implemented by the game devs.
Do you have any specific examples of this problem?