It's not as pain free as Steam, because you sometimes still have to apply wine fixes, but it works well with the most popular games.
1. it doesn't (at least recently?) always do a great job of handling multiple displays, either launching games on my second monitor, which I orient vertically or getting confused about which monitor to use and switching back and forth until eventually the instance (but not the Lutris client) crashes
2. I find myself getting into launcher hell where I'll use a different wine version for one game and when I switch to a different game, it's using this new wine version and stops working
Not sure if Heroic solves these issues but I would try it again (didn't have any luck setting it up initially) if it does
If you are using KDE then there is a global Window rules setting and Heroic actually obey those rules, so you can force to launch a game always on X display, always minimized etc.
https://docs.kde.org/stable5/en/kwin/kcontrol/windowspecific... (not sure that's the most up to date manual)
It looks like gamescope has it's own fullscreen shortcut (super + f), but people complain about it about it going to the wrong display. Maybe your window manager offers a more consistent full screen option like i3 does.