Doesn't it also increase the influence of existing shareholders? People have to decide to sell. It's really no different (to them) that they sell on the open market or to the company.

I'm not defending share buybacks, for the record. They're only one piece of the puzzle however. The real issue is what companies should do with profits and that includes share buybacks and dividends. You can't really be against share buybacks without being against dividends. And tit's fine to be against both. Being against one but not the other is kinda silly though.