Kirk deserved better. Yes, he dies alone, but there is zero sense of mourning. Just another day at the office for Picard.
But why would Picard mourn him? He didn't know Kirk any better than a random redshirt (Kirk is my favorite character). What confused me was that they didn't seem to give a shit that the Enterprise
Even if he hadn't recognized Kirk (which he did, by the way), I would have expected Picard to at least mention to his crew that he had help (he doesn't) from another Starfleet Captain. Add Kirk's legacy back in, and it's criminal.