My main putting putter is the Warden, which is not quite as deep as other putters. I never got into deeper feeling putters for putting, though some are okay for me for throwing. I also like the Colt and Stud, and the Magic that I tried was really nice as well.
One "pro" of a shallow putter: if it's comfortable for you to throw, that's 80% or more of the battle right there. A more comfortable putter will be a putter you want to work with more, and will get better with as a result.
One possible "con": shallow putters tend to be a bit faster than deeper putters, might skip or roll away from the basket more, and further. Deep putters CAN do that, but my Rhyno generally sits down while the Harp and Stud get frisky at times.
I also think my Star Stud cuts through the wind fairly well, and the Harp definitely does... but the Rhyno is a decent putter in the wind, as well...