Presumably no e-stop? No spindle on/off or speed control? In general, it's better to avoid any more connections (=potential points of failure) as you reasonably can, but electrically I guess it will work. Be very careful about ensuring that all the proper ground connections are in place as you appear to be only switching signal connections.

Has anyone done it before? In the sense that there is little new under the sun, probably, but I doubt that many people have as there doesn't seem to be a good reason to do so, generally speaking. I have heard about people switching a single controller between different machines to save having, for example, two PCs in the workshop but that's the other way around.

Again, generally speaking, users decide on their chosen controller hardware and compatible software, get to understand how it works, and stick with it. Switching between different user interfaces is likely to give you more problems than switching the hardware! Yes, Mach3 is a whole lot more powerful than GRBL. In fact, GRBL isn't the issue here as you do not interact directly with it. You actually have to install and run something like Universal Gcode Sender (UGS) to provide the user interface. UGS looks a lot better than when I tried it some years ago for a special-purpose machine (that needed a modified GRBL) but in essence it is a cut-down version of what Mach3 or any other CNC control programme provides. However, as with all software these days, a large part of the task of getting to know something like Mach3 comes down to recognising those bits that are important and those bits which you can safely ignore, at least for the time being. I am somewhat concerned that the problems you have with Mach3 are due to not being familiar with some of the basic CNC machine processes, like how the coordinate systems work, setting work zero, and things like that. Those problems do not go away if you change the control software. I am saying this because I have spoken to and read a number of threads from people in a similar position. I was in exactly the same place myself when I started out, but you quickly get the hang of things with a bit of concentration and maybe a helping hand or bit of advice from time to time.

I would seriously suggest that time spent getting used to Mach3 and its little foibles is more valuable than spending time changing hardware, and will repay you in the long run.

I would also add that I am not knocking GRBL/UGS in any way - there are plenty of people who love it, and the whole concept of "free open-source". But you have already bought Mach3!

Good luck whichever way you go.