It’s not quite what you asked, but when I was in grad school an awful lot of lab glassware – especially custom pieces – were handmade by glassblowers.
I can’t believe that the vast majority of glassware is hand-blown. All those Erlenmeyer Flasks and Florence Flasks and the like are too numerous and their production could easily be automated.
As far as volumetric flasks go, the reason there’s that long tubular section is because you account for variations in the manufacturing by using the position of the scribed line to show the volume – and there’s no reason the flask can’t be machine-made, then calibrated. I would be more inclined to make a machine-made pipette than one made by hand, myself.