With all of time and space to play in, there’s no reason not to indulge the occasional whim, and the Doctor’s indulged this one with each regeneration. It provides a permanent record of every face he’s ever had.
Naturally he picks a different artist each time, he has plenty to choose from.
If he gets bored sitting while the artist works he can take off for a few months, come back the following day for another session.
He pays handsomely for each portrait, hanging them in the TARDIS. It’s almost a shame nobody else will ever get to enjoy them.