Honor is not bad, it's just that some other trees are more useful. It's good with Tradition combo, useful for some civs (mentioned above) or if you plan medium\heavy warfare.
If you have close aggressive neighbor like Zulus or Huns, Honor can be very useful (getting GWG, experience or discipline). It stacks perfectly with Heroic Epic boosts which are easy to build for small Tall (Tradition) empires.
It's must for Mongols and Zulu, since that faster experience makes their units (Keshiks and Impi) fly through promotions.
For autocratic civs, Professional army and finisher are very useful, when you have lots of units that need to be upgraded and if you're doing some heavy killings.
So in general, Honor is not a bad tree, it's just that some others are more useful in any situation. Not a bad thing to open it, so you can get that extra damage on barbs (and also makes barb hunt easier), then switch to either Tradition\Liberty, then finishing Honor as second tree.
mostly it's the "military caste" policy that I think needs to get changed. Honor is for being aggressive, but for this policy you need to keep your army in your cities to get the happiness. It's really not very helpful because if you ever to need to move out, you have to make up that happiness. The culture is pretty nice in times of peace, but honor should not be creating incentives to play peacefully, that just doesn't make any sense.
Nope, that's not a problem. Most of the players will keep archer\cannon inside their cities just in case something goes wrong (like AI deciding to backstab you while you're busy fighting other AI) so that happiness\culture bonus is not a bad thing. It also goes well with Traditions "Oligarchy".