Well I did say it wasn't the best analogy. Would you be ok with a recast first Doctor in a reboot of the universe?
A more relevant question is if we'd be okay with a reboot of the universe. And while reboots have their place as a legitimate story device, I question if such a thing is truly necessary in Doctor Who.
But regardless, if a reboot is actually done, then what the hell, go crazy recasting any incarnation of the Doctor.
if you only like the Doctor for the actor who portrays him, doesn't that mean that you would disdain a novel with the character in it? Because the writer is trying to do an imitation of the character, trying to capture the mannerisms and voice ( a good writer, anyway).
That doesn't really compare though. When watching or listening to a different actor portray a character, I tend to be distracted making comparisons between them and the original actor. And the littlest thing, be it something to do with the actor's voice or appearance can be enough to completely pull me out of the experience. With a novel I can easily imagine the actor no problem provided they aren't written too much out of character. I can only imagine having a problem with a novel if it did something like having the First Doctor hopping around the console wearing a scarf and multi-coloured overcoat screaming "Fantastic, bow ties are cool!"