I practised TM for several years in the mid 70s. Looking back with my current experience, it seems to me that it was quite an effective concentration practice that I am sure had some beneficial effects then and now. Unfortunately, the surrounding ideas became increasingly odd (yogic flying, etc).
Strangely, after a number of years of Buddhist training, I find the mantras rather ineffective. They just don't "hook in" like they did in the old days. As I recall there was a kind of "blanking out" that occurred, and I ssuspect that the mindfulness I've developed prevents that from happening anymore.