I think the history of the origins of welding the neck is now lost. It used to signify the neck being placed different because of a special request (usually by a Pro) and that made it unique and subsequently more desirable.
I prefer a cleaner look myself.
I'm not a history expert on the old putters but I don't see that many Truett putters, Tad Moores, and John Byrons with obvious welds even though quite a few of them will have been welded.
Can anyone place a time period when welds became "en vogue"?