I've never seen an old school fan demand that the show be ended completely. The only people who were calling for Doctor Who to ever end completely were actually some of the hardline Ten/Rose shippers among the new generation RTD-era fans, who spent much of 2009 calling for the show to end completely with the Doctor turning himself human to live a normal life with Rose, so that their ship could be "endgame".

(It's those same people who then went and started the meme of Moffat as Most Sexist TV Producer Ever, because they were convinced that RTD wanted to give them that romantic happy ending and that Moffat did something evil to stop him. Which is why I'm particularly annoyed with that view of Moffat, as I find it hard to see Ten/Rose as in any way a feminism-friendly ship.)