There are A LOT of great composers in the present time (Thomas Ades, Pascal Dusapin, Arvo Pärt come to mind) but their work is less exposed to the public eye due to being less "listener-friendly" than the classics of centuries past. Also it is much, much easier for musicians, directors, labels etc. to get successful with the big names and/or big schools for obvious reasons. Well that's not quite true of Arvo Pärt who is extremely successful.
Keep in mind that recording Mozart's Requiem of Bach's Cantatas for the billionth time is not merely doing a "cover version", but entails (for anyone seriously involved anyway) huge upstream work in musical research, interpretation of the scores, planification, rehearsal, etc. Even the most famous stuff is still open for debate and fresh rendering. None of the old works is set in stone, every one of them keeps moving with the times.
Take these two versions of the Summer, both are true to Vivaldi's writing and notes, but they are almost two different pieces...
[ame="http://www.youtube.com/watch?v=pe-MIDDfckw"]http://www.youtube.com/watch?v=pe-MIDDfckw[/ame]