lubwak: TLDR; It's not only in its potential customers' interest, but also GOG's to challenge Steam on this one. Galaxy support for Windows 7 would definitely help, but I realize it is unlikely.
You do not seem to understand how modern software development works. Nobody nowadays reinvents the wheel for standard solutions from scratch. Apart from additional functionality like downloading and installing software from different stores, at it's very core the Galaxy client is nothing but a customized web browser. And do you really think anyone would program a new web browser when CEF (Chromium Embedded Framework) is readily available?
But the problem here is: Once you include thrid party software into your own software you are dependent on what they support. Or in other words: If CEF decides to drop Win7 support then Galaxy will have to do so as well.
Because GOG can't just take an old CEF version with bugs that are known security problems since they will be held responsible if people using Galaxy will get hacked left and right. So they will be forced to upgrade CEF regularly. And they also can't afford to rewrite CEF to make it Win7 compatible. They don't have the resources for that.
So there is nothing GOG can do about it. Once CEF drops Win7 support there is no way Galaxy can support it.
BTW, can you guess what else is using CEF? Correct. The Steam Client as well as the Epic Client.