You'll hit build issues, bootstrap issues (at which point you'll likely need an old Linux on a VM), kernel issues (which will force you to either patch the kernel, the libc, or both), and then a myriad of desktop integration issues, which is as usual the pain point and the main reason I always say static linking is absolutely useless for forward compatibility. For example, the game will try to set a rare resolution & refresh rate using Xrandr (good luck!), or will try to use OSS (for which user-space emulation with LD_PRELOAD is almost always useless, the in-kernel one prevents you from using pulseaudio, and CUSE doesn't support mmap which a shitton of games use), or even expect some specific behavior from the window manager, etc.
With more recent software, you'll hit issues with the software expecting some D-Bus services e.g. such as project utopia (yet another Linux desktop compatibility disaster that has been quickly forgotten by everyone involved, except for the software that decided to embrace it and now will never run again). In these cases building the libraries is only half the way...
That said, it's still true that a lot of times having the source available for all the underlying libraries is what makes these things possible _at all_.