I don't know about lazy, but he doesn't seem to have your best interests at heart.
If you put another layer on top of your existing floors, you will have to have all your doors taken off and cut shorter, and either refix the skirtings or have an ugly join and fillet.
I would not expect to see noticable gaps at the short ends of flooring unless the fitter was unskilled or the boards were poor quality and did not line up (this can happen with "job lots" of flooring; another sign is lots of short pieces in the delivery)
I presume you are going to spend a few thousand on the floor, so I would want it done nicely.
If you are putting boards straight down onto the joists, they are usually 18 to 22mm thick, and must be in long pieces (2 metres or more long mostly and a minimum of 1200mm so they stand on three joists)
If you are putting engineered on top of a sound floor, 15mm thick will do.
If it was me and I had a problem with cold and draughts, I would take them up, insulate between the joists, and put down 18mm WBP ply; or real floorboards if I could afford it.
Ordinary flooring ply is very rough, with cracks and live or dead knots on the top, I was lucky enough to get fair-faced 18mm WBP hardwood ply from Wickes, my joiner and I selected the best pieces from the stack and loaded them onto his van. Stained and varnished, it looks like the deck of a boat. I have the skill to grain and stain it to look like planks though. Rougher stuff will need carpet, vinyl or (at least) laminate on top. If I was going for a hardwood floor I would miss out the ply and get a carpenter in to lay floorboards (it would be rather expensive). I wouldn't think it sensible to lay a new ply floor and then another new hardwood one on top.
Avoid chipboard flooring.