Did they make a template of the wall? or take detailed measurements when the worktop, upstands and wall units had been fitted? I'd want it to go up to the underneath of the wall units as you say, then seal it with silicon to the wall units so no steam can get in. If its their measurements then its up to them to resolve to your satisfaction. Does the receipt show the actual glass measurements or the size it should of been to fit under the wall units. Personally i think the fitter could see it didn't fit properly thats why he was asking you if it was ok and you were happy with the position etc. Trouble is it will be a nightmare to remove the glass and it will damage the wall when they do it.

I’m an avid cook and had a massive kitchen with two hobs which were never enough so I bought three plug-in induction hobs. I found that I used these much more than the normal hobs as I could cook in different parts of the kitchen as well as outside. I’m now having a house renovated and decided not to have a hob at all as I have limited workspace so I’ll be using my plug-in hobs for all my cooking which suits me just fine. My project manager and the kitchen fitter think this is completely off the wall but it’s something that’ll work for me so I’m going with it. I would hate to have a kitchen with limited workspace and what we would have with a normal hob would be pretty minuscule. It’s not for everyone but the plug-in hobs have been a complete game changer for me and I love the fact that I can stick them in a drawer when I’m done with them

The worktop fabricators will generally refer to the quartz manufacturers guidance, and best practice is of a maximum unsupported overhang of 30cm. If you ever had a problem you may find any worktop warranty is null and void if you disregard this. In the image it looks like you still need a back panel, and you could simply space this back from the units to achieve this maximum overhang?

You can get worktops made to any thickness, granite and quartz usually comes in 20 or 30mm thicknesses but it can be made to any thickness and with different edge profiles, the underneath is packed with mdf and all the edges are made thicker. You can also get laminate worktops made extra thick by a laminate fabricator [google for a local fabricator], they would get/make the base board [chipboard] to your thickness and then bond the laminate sheet to the tops and sides [square edged]. There's also concrete worktops which can be cast to any thickness, copper and stainless steel worktops can also be made to any thickness. Also real wooden worktops can be made to look thicker by a decent kitchen fitter or carpenter.