What's the reason for this?
To avoid the possibility of Chametz as much as possible. Technically the only wheat on Pesach anyone who doesn't eat gebrochtz would be Matzo, so makes sense that they would want to be careful the most with that.
It seems it was relatively common at a certain point in Hungary and Galicia, with varying degrees of either not eating Matzoh on Chol HaMoed, or not eating at all besides the Kezaisim. There were some who very against it, both because of Simchas YT and because of Seudos/Lechem Mishne issues. Others were very supportive. I wouldn't say this was a widespread Minhag among the Hamon Am, it was mostly Rabonim and Rebbes who took it upon themselves. It did seem to originate prior to Chasidim. It definitely was done by non Chassidim in Hungary, too.
