That's not why we have to file alternates. The reason for that is the FAA wants to force idiots to carry more fuel than they would if they weren't forced to carry enough to have reasonable minimum safety margins. There is nothing in 91.185 even suggesting, no less requiring, that one go to one's filed alternate after missing at their destination in a lost comm situation. In that situation, you've flown past the limit of the regulations, and you do whatever you think best to end the flight safely.
ATC doesn't even get your alternate on their strip, so they'd have to do some digging just to find out what it is, and even then, you may have selected it not because it was necessarily where you wanted to go if you missed at your destination, but because it was the first airport which met the legal requirements for being selected. For example, if you have a non-WAAS GPS, you might want to divert to a closer airport with better weather that has only a GPS approach, but couldn't file it because you can't use a GPS approach for your alternate if you don't have a c146 WAAS "sole source" GPS.
Not just "can," but "shall" do so.
In what FAA publication did you find that idea? And what controller is going to care what you used for your routing to your filed alternate?