Grout is NOT allowed to change directions. So long as the grout stays on the same plane (horizontal plane = the floor) the grout is fine. The caulking is the appropriate product to use when moving from horizontal (the floor) to the vertical (the wall) plane.

The builder did what builder's do. They took a short cut based on the availability of the trades. In HIGH END builds things are done in the 'correct' order (correct = best possible outcome). In theory (ahem...not in the real world) the baseboards are done last. But that rarely happens with the vast majority of builds.

The baseboard/grout thing isn't a concern. They did the correct thing by using caulking at the change of plane. What is missing is a continuous bead of caulking. There's some missing in your last photo. These little things make it to your touch-up list.

You will take a role of blue painter's tape and tag all the little issues that you find. You will do this the day BEFORE you do the final walk through with your builder. You will take photos of these items (room shots) after you have finished your walk through. The builder will then have his touch-up crew go around fixing the things that are on the list/tagged with blue tape.

Be prepared to spend several hours in the home that night. Bring a picnic basket and refreshments (leave the adult-pop at home...you want a clear head for this). It can and should take a while.

By can’t change directions, do you mean if there are areas where they tried to fill a vertical gap up to the baseboard then that needs to be fixed?

They do still have to run caulk along the entire floor, I’m hoping I’ll be happier with the finished product but right now I’m pretty upset.

Grout must stay on the same plane. If they 'filled' the gap with grout (they built UPWARDS and NOT caulking) then it should be looked at. If they used ++grout ON THE FLOOR to fill a gap to the wall (staying on the same plane) then no. That won't have an issue....because it did NOT change directions.

I'm assuming you are referring to the 1" worth of grout on the floor (where you think a SLIVER of tile should be)? Technically (that means structurally) this is 'fine'. Aesthetically it isn't the best option but it is probably MUCH better than a sliver of flesh-shredding tile.

Basically it isn't pretty but it is probably the best they can do...and the grout is most likely going to be quite safe.

Is there a way to fix the way that looks? I have that at my house and I hate the way the grout at the baseboard looks. Is adding quarter inch round trim the only option (without replacing all the baseboards? There is grout cracking all along the baseboards in almost every room that has tile.

I'd grind that grout out before the tile "tent" and cover the gap with shoe mold.

EJ 171 violated. And just bad builder level quality tile work in general. Id be far more concerned with the (lack of) waterproofing in the wet areas.