How much of a gap are we talking about...exactly?

Caulk or shoe mold.

Here are photos. Prefer not to have shoe molding

If you don't want shoe, all the molding has to be pulled and scribed to the floor. Carpentry 101.

I thought that is what they would do to begin with. Apparently not. Very disappointed!

Scribing the base to the floor would have been roughly 5x+ as much again for the quote to just slap it up and cover with shoe. I'm sure that you can find someone to do it but it won't be flooring installers. It will be an actual finish carpenter. With a small project premium. Maybe save up and have other molding projects done at the same time so the economy of scale can lower the price a tad.

The flooring does meet the wall. We had the contractor handle the baseboard molding and not the floor guys ~ Thinking incorrectly they would do the best job. We do not want to use a shoe molding - had expected this to be flush.

How about a thicker molding style that would cover the largest gap?

homepro-

I think the issue the OP is concerned about is the gap between the bottom of the molding and the top of the floor, which would not be addressed with thicker molding.

Kudzou9 you are correct.

I went through the same thing - in the end , shoe molding went in.

Is there a gap all the way around the room or do the baseboards rest on the floor in places?

If you put a level on the top of the baseboard, is it level?

You could caulk or putty/sand/paint the gap, though it won't likely look perfect (i.e., like wood). How big is the gap?

The baseboards lay on the floor in some places. I'm not on site now so can't see if level.

I suspect you will find that it is like any large dimension baseboard: even a well-laid floor will have subtle undulations and the bottom of the baseboard will rest on the high points causing gaps at the low points, unless scribing is done.

The baseboard will be level - or close to it - if the floor and subfloor are level. The issue of being absolutely level is not as critical as the irregular gaps that one sees if shoe molding is not used.

Yes it's the gaps that are getting to me. Shoe molding it must be I guess.

Flooring is not supposed to touch the wall normally, so it can expand and contract. However if they installed the baseboard and there is still a visible gap when looking straight down, its not a great flooring job IMO. Now if the floor is uneven I would understand a small gap visible when looking straight parallel with the floor, but it should be a negligible gap.