I don't know who invented the remix (but I know it wasn't Puff Daddy) but in the 1970's some disco DJ's started producing own extended versions of tracks with longer intros, breaks or endings by copying and pasting the relevant parts using tape machines or by live mixing two copies of the track (although this may have been inspired by the way reggae producers made dub versions of tracks by removing the vocals and adding sound effects). When bands, producers and record companies found out what they were doing they started to produce extended versions and released them on the new twelve-inch vinyl single format.
It was only after hip-hop's pioneers started sampling and changing tracks and bands that used synths (such as New Order, Depeche Mode and Soft Cell) realised that their music was being played in discos in the late 1970's and early 1980's that artists or record companies started getting other people to produce a different version of a track based on parts of the original recordings. Sometimes this was done because artists wanted to know what other people could do with their work, sometimes this was done because artists or record companies wanted their music to be heard by people who wouldn't normally hear it and sometimes this was done to fill up twelve inch singles without writing new songs (another trick that was used at least once to help fill up a single was to put a backwards version of the A-side on the B-side, give it a new title and claim royalties with minimum effort).
As music technology got better and the club scene got bigger remixers became more ambitious, using less and less of the original track, changing the original tracks more and putting in more sounds from other sources (although ironically one of the first really famous remixes, Coldcut's "Seven Minutes of Madness" remix of Eric B and Rakim's "Paid In Full", was made by live mixing the original and various other tracks such as a track by Ofra Haza). By the early 1990's remixing had become an art form in its own right with some DJs producing great dance tracks using very little of the track they were remixing and lots of samples and music they had made themselves (such as Primal Scream's "Loaded", Andrew Weatherall's radical remix of "I'm Losing More Than I'll Ever Have").
So what's the big deal about remixes? You're right to say that some remixes contain nothing original at all which is true of some early remixes (such as some of the remixes of NO tracks made in the 1980's) when there was little that people could do to change a track. You're right to say that some remixes are boring which is true of some more recent remixes in which the vocals are placed over a bog-standard dance track (such as the Perfecto remix of NO's "World" which is very similar to the Perfecto remix of U2's "Even Better Than The Real Thing" - if there had been a Perfecto remix of Frank Sinatra's "New York, New York" it would probably have been very similar as well). You could also say that some songs contain nothing original at all and some songs are boring.
However, some remixes are so original that you can barely tell which song has been remixed (a few years ago some remixers began claiming that they put so much into their remixes and made previously unsuccessful songs into big hits that they should be credited as producers and paid royalties rather than just paid a one-off remix fee). The best remixes can be almost as good as the original (such as the Fire Island mix of New Order's "Regret", a house remix which really suits the song), as good as the original (such as Paul Oakenfold and Steve Osborne's 12-inch remix of The Stone Roses' "Waterfall" which sounds like an alternative version of the original on which John Squire and Mani play a different intro) or even better than the original (such as Norman Cook's remix of Cornershop's "Brimful Of Asha" in which he took the flat-sounding original, speeded it up a bit and added a new rhythm track to bring out the joyous quality in the song). Some remixers and remixes aren't worth bothering with but some remixers and remixes are, just as some artists and songs aren't worth bothering with and some artists and songs are, and when you hear a few by someone you decide whether or not you want to listen to more by them in future.