It seems like you are trying to ask "Are there songs/tunes/pieces where every chord has the same root note?"
I have some problems with some other things you said - Is it 'considered' a 'valid' chord progression, uh, which either I misunderstand or you radically misunderstand the nature of these things. I'm not sure how music can be 'wrong', like people say. What is 'wrong' one day is the brilliant innovations of the next generation; surely almost everything is 'OK' nowadays, if you like it. I don't know what that would mean, 'wrong'. I've even heard musicians talk of a chord progression 'not making sense', even though it sounds fine, because supposedly it doesn't do what theory says a progression should. Who cares. Music theory is like grammar. It's just (or was initially) the ways people speak/write, or the harmonic progressions etc that sound good, written down in a book. Where else could it come from. I don't know what else 'valid' could mean, other than it's approved by these supposed authorities. Like has been said already here, in music, if it sounds good, it is good. There is no other source of 'validity'. In short, don't worry so much. Play what you like, study and learn from what you like. Etc. :-) Less caring what is 'valid' or 'wrong', more 'fiddling around with chords'! :-) Knowing what something sounds like is more important than knowing what it's called, but sure, it helps when trying to write it down or communicate it to others. Good luck.
I can't think of a piece using that exact pattern, but I'm sure it would occur a lot in classical, pop/rock, songs of various genres. Just usually it wouldn't be written in the chord symbols, but just occurs 'naturally' when melodies pass over chords. Yes, it's weird to see something like that written out, but not to hear it.
I guess you just like subtle harmonic changes. You could try playing any 'conventional' chord progression entirely over the same root note. (uh, why not D hehe - write in here and ask whether it's a chord progression although it's all D chords haha) This kind of thing often called a 'pedal' (at least in classical/rock/jazz) - a D pedal (from organ pedals, I guess) with various flavours of harmony passing over it.
To actually answer your question, well yes, I've heard pieces in jazz, also in blues, with the same key/root note throughout. Also, I don't there is a clear line between 'chord progressions' that are all in one key (e.g. D) and ones that aren't, strange as that may seem. What if one of them is an inversion? like a D triad but with F# in the bass - do you count that as a D chord? No? They have to have D in the bass? Well, how about an Eb triad with a D in the bass? Eb/D? Or the various other 'slash' chords. So I don't think saying 'A chord progression is when you play different chords' actually draws a clear line the way it's intended to.
I hope this was of some help. :-)