Typically, the cabinet installer installs the built in appliances and that's NOT included in the "appliance installation". Appliance installation is for non built ins. Like a free standing fridge that rolls into place, or a simple DW install that doesn't involve cabinet panels. Or sliding a range into place.

And yeah, that's about the going rate for a built in fridge install. And you DO have 2 of them.

Our GC installed all of our appliances, including 2 Thermador columns with door panels. The install price you were quoted is about the going rate based on info I got from the appliance store.

If your GC's contract says he will install all appliances, he needs to do that or reimburse you for doing the job you paid him to do that he's not doing.

Yes, it's a reasonable fee.

If the contract was signed without the appliances being selected yet, then I wouldn't expect the GC to absorb the fee for installing any built in appliances. It's a lot more complicated and takes much longer than standard consumer grade stuff that just gets plugged in and slid in place. Time is money. Not everyone has the skill set to do this. He was probably expecting standard consumer grade built in appliances.

If, on the other hand, y'all drew up the contract where the appliances and their specs were part of it, and now he sees that he doesn't have the skill to do the job, I'd want him to refund the amount out of the contract to cover the other labor to do the job. And, I'd also want to be taking a fine toothed comb to the project. If he's not comfortable having the skills to do the built in appliances, I'd want to know what else he wasn't really skilled enough to do but was able to BS his way past on the job.