That removes paladins (LG),
Indeed. I can see two resolutions to this: have "Holy Warriors" of all alignments of (my preferred choice) make the Paladin a PrC.
I would drop the alignment restriction. LG druids might be a bit of a stretch, but if we can have CN and NE druids, are CE druids so much of a stretch? Likewise CG doesn't seem to big a deal. I'm not sure about LE. However, I don't see too much hardship in removing the restriction.
(Plus, of course, many games drop alignment entirely, and have Druids working out just fine.)
Barbarian/Beserker (Nonlawful),
I find this one a bit more problematic - the notion of a Lawful barbarian srikes me as somewhat jarring. I'm sure there's some way to make it work, though. (Besides, I'm halfway inclined to say we don't need both a Barbarian and a Ranger class, and that Rage should be a talent tree or feat chain.)
Rename the class to "Unarmed Combatant" and non-Lawful Monks fit a whole lot better. I've found that the Monk class is very good for representing certain pirate types, and (in particular) an Orcish street-brawler. Neither concept is particularly Lawful. I'd ditch the alignment requirement (and rename the class).
Someone suggested a "Knight-errant" Paladin/Bard concept that sounded workable, except for the alignment restrictions. The basic upshot is that I don't think Bards need to be non-Lawful to really work as a class, so I'd drop the requirement.
Okay, you've got me. I think the Knigth should be a PrC anyway, but there is a niche for that sort of warrior (that also includes Samurai in my view of classes BTW). And the nature of the class would seem to require a Lawful alignment.
Perhaps the solution there is to have some sort of 'Cultured Warrior' class, that can be used to represent the Knight, Samurai or Swashbuckler. Such a class would have medium skills, configurable good saves (say Fort + either Ref or Will), good BAB, and a bunch of talent trees related to being personable. Of course, the choice of following a code or not would then be up to the character. (Armour use would be one of the talent trees, or handled by feats - but that gets into how I would handle AC in a new version of the game, which is wildly off-topic, so I'll stop.)
I suspect that's probably a step too far in the 'broad classes' concept, though.
Warlock (Chaotic or evil),
Again, I reckon the alignment restriction is pure flavour, and you could almost posit a Warlock empowered by forces of Law and Goodness. There might need to be a slight expansion of the Invocations for this to work, but that's no bad thing.
Far too narrow a class to justify it's existence anyway, IMO.
hexblade (nongood) etc...
This class is banned from my games because of the alignment restriction (I only allow Good characters at the start of a campaign). But I see nothing in the class that is inherently non-Good, and can't be made to work without the alignment restriction.
Basically, my principle is that base classes should be nice broad building blocks for characters, unbound by the campaign environment. The designers of the game have no idea what my campaign looks like, so should design accordingly. There are certain roles that will feature in anything but very odd campaigns (Fighter, Rogue), and some that exist by virtue of their place within the rules systems elsewhere (Wizard, Psion).
By that logic, a Samurai is either a Fighter or 'Cultured Warrior' with particular choices of feats/skills/talent trees. A Wu Jen is either a Wizard with particular spells or a reflection of the new variant magic rules are added for the (theoretical 4e) Oriental Adventures supplement. A Swashbuckler is a Fighter or Rogue or 'Cultured Warrior' with different feats/skills/talent trees.