I first had MDMA when it was still legal, in the 1970s and have probably taken it a dozen times in my life.
Thing is, it's not a drug that is conducive to sitting in dark silence. It's not as speedy as the last two letters (MethAmphetamine) would indicate, but it's still a stimulant. I have never enjoyed it fully for that reason - I have to work fairly hard not to grind my teeth, for example.
It's a very active drug, which is why people want to dance and have sex.
Classing MDMA is a psychedelic is problematic and give a poor idea of its effects. Classic psychedelics like psilocybin mushrooms or LSD produce dramatic color effects and closed-eye visual patterns, which are mostly absent from MDMA. Someone, I can't find the original source, suggested it be classed as an "empathogenic stimulant" which seems pretty accurate.
And as others have noted, MDMA leads to a serotonin hangover which can make depressed people even more depressed.
Don't get me wrong - I think that MDMA is an extremely promising drug for therapy but it's not some magic bullet that you can take and will instantly fix you up.