Alexander Armstrong is posher than Prince William.
It does matter.
And you're right, it doesn't matter whether they're gay / Asian / etc. The point is how their voice / look / mannerisms go down with the audience.
A lot of viewers dislike the voice / look / mannerisms of 'minority' presenters. But no sane person would suggest banishing those presenters from a TV show just to appease the terminally prejudiced. You however seem to be advocating discrimination based on class, and in my opinion that is equally unacceptable. What would you say if I suggested that a Geordie wasn't suitable for presenting the One Show because some viewers in Surrey might have a grievance against northerners?
I can only speak of my own perception but I would say that Alexander Armstrong does have a rapport with the audience. Many viewers probably see him as a figure of fun without feeling resentful because of who he is. And then of course there will be some viewers who vanish in a thick cloud of moral vapours every time they see a 'toff' on TV - just as some viewers do when they see Paul O'Grady, for example - because they are not at peace with themselves and as such, cannot, or do not want to see past another person's background, race, sexuality or etc. But that is their problem, not anyone else's.
And for the One Show's audience it appears to me (not necessarily to anyone else, but this is a forum after all) that it's a strange choice.
And Matt Baker may be "delightful", but I think the programme is missing a trick in employing someone who is so anodyne that I for one don't care if I miss the show.
So let me get this right... you think Alexander Armstrong is too offensive but then you end the post by saying that Matt Baker is too inoffensive. Just who would you like to see presenting the One Show?