Hmmm, let me see - famous great authors/playwrights - who are just as well known as the actors who interpret their works? Well what about -
Arthur Miller, Edward Albee, Jean Giraudoux, Joe Orton, our own -
David Williamson. Then there's Alan Bennett (The History Boys), who's caused quite a stir and brought audiences to their feet the world over and been lavished with awards...

As someone who is both I think you're all kinda right. I also think it depends on the medium.

Apart from docos I have only ever written for stage and radio - and there the writer certainly gets the kudos. I have to admit that at times I have been horrified at who has been chosen to play some of the roles I've written. But then you hear/see them at work and you suddenly see facets of your own script that you didn't even realise were in
there.

As an actor I have, once or twice, been given a script that I thought was absolutely terrible - as have the rest of the cast. Yet those have sometimes been the greatest success of all when they are actually produced.

As for things like "Friends" etc. well strictly speaking there is no one actual writer for many teleplays. Anyone can send in a script for many of them, other employ teams of writers; some "brainstorm" with a group of disparate people and still others have a general outline which they, in concert with the actors, develop as they go along.

The really great story-tellers of the screen are, by and large, very well known and revered - and certainly carry a lot of weight, money and kudos as a result of their talent.

But as for writers being shy introverts who shun the limelight? Yeah.
In yer dreams.