Here's my theory, and it goes back to Cameron. The first 350g production putters I know of where the 33" gun blue Titleists, that were marketed as being for women. Same with the later OC version. They became very popular with shorter golfers who wanted 33" putters. These putters became very popular in Japan, where Camerons were already avidly collected. Then custom and "tour" models started popping up with these specs, and it wasn't long before 33/350 was called "tour preferred" (even though it wasn't). US collectors hopped on the wagon. Interestingly, Cameron was always adamant that his putters were correctly balanced at 36/320, 35/330, 34/340 and 33/350. But, when the 009's came out, suddenly there were a lot of 34/350's. Many of us saw that and wondered what had happened to the old balance "rules".
I don't think there's anything wrong with 350g heads. I do think they are better suited to short lengths. I used to use 33/350, during a period when I was stooped over with a bad back. As that got better and I became more upright, 33" was too short and I was back to 35". With Bruce's help, we discovered that for me, at that length, weight in the 330g range was best.
Back to the tour. I would bet that there are very few guys using 33" putters. They are also playing faster greens than we are, on average. IMO, these factors drive the prevalence of lighter weight heads.