Medium format lenses generally don't resolve as well as 35mm ones (they don't need to on 120 film) so there are no real advantages except as above.
Often heard. But not true.
I used to (only sometimes though) carry a 35 mm body (Olympus OM, so a small one) and lens adapter in my MF kit. A small addition, compared to the MF kit.
But i never used it.
I wouldn't do it the other way round, carry MF lenses in a 35 mm kit. 35 mm format lenses are small, cheap (relatively - for the price of one MF lens i could assemble a rather complete 35 mm lens kit) and good enough, given the too small 30 mm format.
See, Jim, that's the origin of that myth.
35 mm format lenses have to be better than MF lenses to be able to keep up, given the small frame of 35 mm format.
That demand for extra performance was, and all too often still is, mistaken, the "should" turned round into an "is". But it's just not true that way round.
Yes, some very good 35 mm format lenses are better than some not so good MF lenses. Some very good MF lenses are better than some not so good 35 mm format lenses. There is no general either one is better than the other situation.
What remains though is that the 35 mm format frame being so small, you're better off using MF.