In fact a number of people do play both systems .....I do. Not because of any innate talent but rather that 25 years ago I couldn't decide which system I liked and I still haven't ! There is no conflict in playing both and I love 'em both.
            However,given the broad range of music you want to try,let me suggest the English.Chromatic,chords but less successful for Morris.
       Anglo is great.....yes more intuitive....but if you want to play tuned with chords you're pretty much tied to specific keys.ie I have a C/G,G/D with a B Flat/F coming soon.
               Also consider a duet,...people say they are difficult to learn but I've seen people play violins....a fiendish instrument,and I've actually seen people playing pianos where one hand is doing something totally different from the other .Amazing!!
Its all relative...if you practice on a duet you'll be able to play it wonderfully.
   Finally ,be prepared for other concertina players to take exception to everything I've said.They are a contentious lot,but unfailingly courteous. I love them too.
          But make sure you play one .
                         Regards Robin