Most phlebotomists are proficient at drawing blood from all age groups. The ones I've had recently have been so slick I haven't even felt the needle press the skin. Yeah, us oldsters have a tendency to develop ropy veins that like to roll and that makes it difficult to draw blood. Sometimes veins can develop scar tissue from multiple draws. That's no excuse for bruising a person up or causing them pain. But trust me, if they can vampire blood out of a newborn, they should be able to get blood out of an oldster like one of us with little difficulty.
I took a course on drawing blood. We were taught 2 tries then hand off to somebody else. If I'm the victim and they can't hit one of my veins I ask for somebody who is good at pediatric draws.
I refuse to be anybody's pin cushion.