You mean Pawlonia tomentosa?.
They do suffer from Leaf spot which leaves yellow lessions.
We cut ours down in February, right to the base. We then allow three buds to delvelop. Those produce thick stems which grow to 15 feet in the season with leaves like elephants ears. The more stems you leave, the smaller the leaves. It flowers at Powys Castle by the way, though last time we were there it looked very sad. We have never lost any buds to frost, yet and as you know we are definitely in a cold part of England.
Tree and leaf