I usually do this if I'm having a real rough day through some holes, switching to something outside of my usual putters like my Skeeter or some other mid helps me stop overthinking everything and just throw it at the chains. I've known a couple people who use mids like rocs/buzzes. I hesitate to say that there's anyone truly "better" putting with non-putters. One friend of mine only has a cyote and a teebird and is a pretty solid player. The cyote is almost a putter itself anyway though, so it's not quite as extreme as using other mids. If you're just playing casually and don't want to carry more than a few discs, short mids can work fine.
There are actually some very good options for shallow rimmed putters, I would highly suggest this over putting with mids. I have a classic roc that has a nice shallow rim, I believe the DD Judge also has a shallow rim and is well liked on this site at least (usually a good sign).