That said, if there was a 6 way title race and you asked people who they wanted to win out of Chelsea, City, Arsenal, United, Spurs and Liverpool I'd imagine most would say City.
Purely impressionistic on my part, of course, but I think it's a bit more complicated:
There are supporters of other clubs within Greater London. Then there are supporters of other clubs throughout the land. Then, there are the people (and they are very significant numerically, and I believe in terms of revenue to the satellite tv companies) who take a passing interest in the PL, don't particularly consider themselves supporters of any club, and have certainly never been through the turnstiles anywhere, but who quite like to watch this and that match on the telly.
I believe that the reactions will be very different to those six that you propose depending on which of the three categories they fall into.
The third category — and I'm virtually sure of this, because I'm thinking of friends of mine who fall into it — have a sort of lazy benevolence towards either United or Liverpool. They submit to the permanent tsunami of propaganda about “the magic of European nights”, “the Busby babes”, plucky Liverpool, glamorous United, etc., etc., etc., ad nauseam, who “play football the right way”, and on a shoestring at that! Oh, and having teams made up of their youth team products, of course. They are told to favour those two clubs, and by and large they are inertly obedient to the order.
Within Greater London it's a different story, I think, but I'm much less sure of my ground. Arsenal fans would, I think, rather anyone won it except Spurs. And vice versa. Chelsea fans seem to hate Spurs almost as much as Arsenal fans do, and my impression is that they'd rather anyone than Spurs, although the prospect of Arsenal winning it does not exactly fill them with glee. Spurs fans appear to hate and look down (God knows why!) on just about everybody. Just my impression. I don't know and have never met anyone for whom Spurs were their “second” team.
When Spurs met Liverpool in the CL final I had a terrible choice to make. I was kind of rooting for Spurs, in so far as I cared about the event at all, but I felt filthy about it.
My experience with fans of other clubs outside London is that they dislike both United and Liverpool fairly intensely, and would rather anyone else from your list won it, as the lesser of two evils. Mainly from having the experience of arrogant — and sometimes violent — fans at their grounds and in their pubs for some forty years (and still now). Those disliked fans are by no means always from Manchester and Liverpool, by the way. Far from it. It's not rare that the billy-big-bollocks fans of United and Liverpool have rarely or never set foot in the north-west.