Not really a problem for me, because knowing how long NMC often takes, I submitted it early and still have several months to go on my current medical certificate.
The doctor fills out the USCG medical form when he does the physical. There is nothing more to it. I usually have an unpredictable schedule with very long hitches in remote places with poor communications. I had one medical certificate get lost in the mail, at least NMC claimed they sent it. It took two months just to get a duplicate. It’s better for me to let an expert with good communications handle the process.