We now have G2a3 from Neolithic Linearbandkeramik in Derenburg and G2a in Treilles in addition to Ötzi from the Alps. G2a folk got around. He joins Stalin and Louis XVI as a famous G2a. It was already clear with the discovery of G2a in France and Central Europe, that this otherwise uncommon present-day haplogroup in Europe was more prominent during the Neolithic, and Ötzi's data point seals the case. In a sense, the triple G2a finds in Neolithic Europe confirm the origins of the European Neolithic population in West Asia, but renew the mystery as to how all the rest of the "players" of the European Y-DNA scene appeared on the scene, with everything except G and I first appearing in the ancient DNA record after the end of the Neolithic.
Yes, I believe that the Paleolithic-Neolithic dichotomy is more hindrance than help in understanding the European past (the Paleolithic itself may have exhibited more population turnover than we can appreciate). I suspect that the two most common European Y haplogroups, R1a and R1b, underwent rapid increase in frequency over the past ~5,000 years. I do not believe that this is necessarily representative of the rest of the genome. The spread of male lineages can be rather unrepresentative. In other news, Ötzi's genome is going to drop any day now. My prediction that it's more West Asian than we might have expected seems more plausible, though less surprising and risky, at this point.
Image credit: 23andMe