I use it all the time. I play rock, pop, country, easy listening, folk, contemporary worship. But, It's not like I actually write out the roman numerals on a chord chart. It's more casual than that. I know that G - E - C - D is a 1 - 6 - 5 - 4 progression and most of the time I can quickly transpose it in my head and often on the fly to a different key by keeping the 1 - 6 - 5 - 4 progression and not really thinking about what the actual chords are, other than the 1. In fact, I don't even know how I learned to do it or what got me started using it. It probably came over time just from changing keys on songs to accommodate my voice or other vocalists. Plus, I pretty much only play guitar so transposing on guitar as many know is often quite simple.

To address the original question: If you learn the notes on the 6th and 5th strings all the way up to the 12th fret and use those notes as your roots that will become easier over time. As stated, capo 3rd fret and play a G shape = Bb. Play a C shape = Eb and you learn to just rename the chord shape in your head according to where your root notes are on the lower 2 strings. Once in a while you'll pay attention the 4th string as in a D shape. Over time you should just start doing in. You'll be able to look at a chord chart in the key of Bb and you will be call your G chord shape a Bb because of where your root note is on the fretboard. Does that make sense?
I used to make note cards, as in, I would write the notes on index cards and shuffle them. The student would play the note on the 5th or 6th string as I called it. They would look at a cheat sheet of the fretboard with the notes written on it to find the notes and play them until they no longer needed the cheat sheet. For most it did not take very long.

Does the noise in your head bother me ?