It would totally work! If you're finding your DT 880s too quiet or perhaps maybe lacking then a proper dedicated headphone amp will be the ticket. Likewise with your MDR-7506s and moving to the Roland. With that said, if you're happy with the headphone output on the UR22 and you need to drive monitors as well then you can. However, it requires that you have the ability to "split" the line output signal. This can be done with something like this, and if you're handy with a soldering iron you can make them yourself The reason this works is because in transferring audio the thing of concern is the AC Voltage. So, as I mentioned in my first post audio systems operates on Impedance Bridging. The fundamental principle in action here is that your audio interface will have a very low output impedance, on the order of a few ohms or less, and the input to any given device will typically be on the order of at least 10 kilohms. This means that very little current actually flows into the receiving device and you're effectively measuring the voltage. Then since the devices receiving the AC Voltage are connected in parallel they will have the same voltage potential across them. It is actually quite an elegant solution honestly.
Your upgrade plan has nothing "technically" wrong with it all. It is very much equipped for the intended purpose of giving you two headphone outputs with one of those outputs having tons more power than you do you now. Whether it sounds "better" is something only you can decide. If I may make one suggestion. Think about what you're going to need in the future in terms of your audio interface. If you want more ins and outs then buy it now. You may have plans in the future for an outboard synth or an outboard buss compressor and those will eat up valuable analog ins and outs. I'm not saying that the Rubix 24 is bad or the like, but it is a small interface without much actual I/O digital or analog. You may be working 100% ITB with maybe a need for a mic occasionally. For that it is perfectly equipped. I know personally I'd be too limited by it immediately. So, just think about what you actually want to do in the future and buy based off that
I've got a fairly complicated setup so I've had to learn to deal with the sorts of issues that pop up. I've had to deal with ground loops, bad cables, not enough I/O, varying power voltages, etc . . .. This can be a complicated mess to sort out. So, if you ask me a question about the "technical details" I can probably explain it. However, when you start getting into subjective things like will it sound better or the like, well only really you can decide that. I mean there are some obvious things like if you want more detail in the bass region then you've got to do the whole room treatment things and get bigger/better speakers. There really is not an easy way around that sort of thing. However, if you want to know why your square waves don't look like square waves on an oscilloscope in the real world or connecting things up. I've got you covered.