I believe some basic magic items should be in the PHB, such as flaming weapons, or holy weapons. I mean anyone playing a paladin things to themselves at character creation "Man, I'd love to have a holy weapon!" That and things like flaming weapons are pretty much staples of the genre.
The cat's out of the bag guys, trying to put it back in just isn't going to happen. Anyone who's played before will know there are magic items regardless of what book they're in, and anyone with an internet connection be be able to look up a list.
If the DM wants to restrict what magic items are available, the DM always has that power.
It is however nice to know what types of items my players would like to have to better enhance their character concepts. Then I can work in unique and interesting ways for them to acquire these.
As for random loot, well, most of my random loot consists of:
money
rope
junk
small trinkets
items the enemy used that were not destroyed in the fight.
So generally speaking, my players only find random loot in chests or treasure rooms, after serious encounters/adventures, so I feel it's OK to give them what they want/need rather than throw random things at them.