Because it would make the character creation process way longer. One of the focus of 5e, among fun and narrative, is the ease of play.
You don't have to look to a list of features that a few splatbooks later become thousands to create your character. Pick a race, pick a class, you are ready to go. In the next edition they are moving subclasses for all classes to third level, in this way a lv1 character is easier.
For the same reason there are not many choices when you level up. At the moment I'm playing a campaign of pathfinder, which is a system I don't like, and every time we level up is atrocious because nobody is interested in the game system, feats and shit, so I have to level up everyone's character because me and the master are the only rules savy of the group. Sadly the master refuse to DM anything else so...
