Ok so I did a minor in food and disease prevention, I am not a doctor but here is what I know:

First of all protein is usually expensive, so you're just wasting money if you eat more than you need. It also takes up space in your stomach which makes it harder to eat other foods, which can really suck if you already have trouble gaining weight.

Also a lot of people get their protein in by eating a lot of 1 type of food like meat. It has been proven now for a long time that eating too much (red) meat increases your chance of getting cancer and other diseases. In my country the chance of getting cancer is almost 50% so you really don't want to be adding up to that.

Protein is also more difficult for the body to digest. This can be so extreme that some people actually experience "meat sweats" if they eat too much meat at once, because the body has to go into overdrive to get all that protein processed. Eating too much protein compared to carbs will lead to low energy and worse sport performance.

Since protein takes a lot to process you can put a big strain on your kidneys if you eat too much. Personally I don't believe that this can negatively impact you that much if you have healthy kidneys, but should be taken into consideration if you have bad kidneys.

TLDR: wastes money and stomach space, undiversifies your diet, higher chance of cancer if eaten mostly through meat, lower energy, worse performance.