The argument for a remake falls down when people say the original film is "dated" and that a new audience doesn't want to see such a dated film.
The source material is dated so what do you do?
Ignore the time in which it was written and set?
I agree with people saying the earlier Pygmalion film was better (Wendy Hillier) and that could be remade as a period piece and audiences will understand that they are watching a historical/period piece.
But how do you translate a musical for a modern audience if that same audience can't watch a version that was made when the times depicted were in living memory?
There is a mass of social commentry, the whole film is social commentry. But of the times it was written.
How will a modern audience who people say don't want to watch a "dated" film, relate to a modern version that still includes the whole idea of only being able to work in a shop if your accent is correct?
And that once the accent and manners are learnt "what am I fit for".
And then they sing a song about it.
In 21C Britain?
It's the fact that it is a musical is where it will fall down. The audience that can accept it being a period piece wouldn't/won't have a problem with the original anyway.
So what audience will the film be aiming for?
Basically there are two ways to do a remake of such a movie.
Either you keep the original setting and keep it as a period piece, which can sometimes work (the recent Les Mis being a good example), but the danger is that the makers can sometimes aim for a carbon copy of the original, which will inevitably look inferior.
But setting it in a modern day setting, which would be my preference, means the story needs to be adapted and changed, obviously. As you say, the social commentary aspect is important, but of a writer can find a way to make the story relevant in the modern age, it can work.
If there are some aspects of the story that simply won't translate to present day, then again that's where the adaptation and writing comes into play.
I always believe that a good, compelling, classic story can stand both the test of time and can also be impervious to an update, if done correctly.