apparently deserting the post of headmaster while the school is in danger is a no-no. i believe that it was mentioned that harry insisted on a snape portrait after things settled down a bit.
snape didn’t desert. he wasn’t even sacked. he just bolted from too many old wands pointing at him. in the shrieking shack, he spoke like he was still head of hogwarts.
Incidentally, if anyone wants to read a fanfic where the “evil mastermind” (not Voldemort) is a portrait, let me know.
I don’t think there is a real problem here, the paintings don’t all have to be equivalent. Perhaps the painter of Sirius’ mother didn’t know here well, or possibly it is not imbued with as much magic, making it more of a caricature. The paintings in the headmaster’s office may simply be of higher quality, and therefore capture more of the subject’s personality.
also the paintings in the headmaster’s office “appeared” when the headmaster died. perhaps there is some sort of thingy that happens when you are headmaster that has a portrait “pop up” that gives it a bit more of a punch than portraits that are done while the subject sits for it.
[spoiler]I think the only reason Dumble’s portrait was useful to Snape was because it was specifically designed to be. And not in a general sense, either. I think Dumbledore likely had it made and “programmed” it with the exact instructions it would later give Snape. That it takes the form of an animated picture is inconsequential.
Phin’s portrait basically just follows instructions.
Edit: And as for Hermione getting a portrait of Dumble, keep in mind what I suggested: Dumble’s portrait was made specifically to help Snape and wouldn’t have been of much use to Hermione. He purposefully kept information from Harry & CO for reasons described at the end of the final book. If he’d wanted to give them a detailed walkthrough he easily could have. Everything that happened throughout the series was by his design. Darth Sidious doesn’t have anything on him.[/spoiler]