The central problem with alternative tunings to equal temperament is that it is not possible to construct a pure scale for more than one diatonic key. And, even then, the requirements of producing pure-sounding chords necessitate having more than one type of Bb, for example. To create pure organic music in all keys, you would need a scale of about 60 microtonal notes. It is just not always practical.
With modal music it is more viable because modal music tends to stay in the one key. You can obtain some good results. You can opt for pure tuning or even some of the more exotic types of tuning found in the world.