ETA at the bottom of this post.....
If I hadn't had experience with this, I might be listening to your dentist, but I do have experience with this issue with my son. You are right.
My son had an extra tooth up above his top front teeth. He was 4 years old. The tooth was the size of half of a molar. They had to remove the two front teeth so that the extra tooth could come down. It took a while for it to come down, and then they removed that.
Our pediatric dentist told me that the other teeth will move around with empty spaces there for so long. Having a partial in there holds the place for preventing that.
My son's permanent teeth didn't come down until he was in the middle of first grade. The dentist explained to me that it was so long because after removing the baby teeth, the bone in the gum gets hard, and it makes it much harder for those permanents to come down.
Other reasons for having that partial are because having teeth there helps a child eat easier. I can't imagine having that big a space for SO LONG with no teeth there to eat with. My son ate everything with his, even corn-on-the-cob. They never came out - they were just fine for eating. Also, speech is a HUGE issue. All you have to do is talk to a speech therapist, and they will tell you that having a partial there will be very important for your child's speech. If you don't get one, you very well may HAVE to have speech therapy for your child later on to fix speech mistakes caused by not having teeth in place for such a long time.
I would find another pediatric dentist, quite frankly, because it worries me that yours calls this a cosmetic thing. It just isn't true, and she should know that. WHY she doesn't would be very concerning to me.
ETA - I just read through a few comments and I want to make sure that I add something here to clarify. My son didn't have ANYTHING implanted. I'm surprised they'd do anything like that to kids, but I don't know about that stuff. It was made to fit his mouth, and wired to the adjoining teeth on the side, like a retainer. It had "gum" around it and looked very natural. It performed just like regular teeth. They never moved around, he didn't take them out, and they didn't cause him any problems. Just wanted to make sure I made it clear that this was not an invasive thing... Now, your child has FOUR teeth being removed. It will be a little different with you having 4 teeth instead of 2. Maybe that's a little harder, but I don't know.
Please get a second opinion from another ped dentist.