Here's a question for ya, Irda Ranger, in all seriousness:
What, exactly, do you find inelegant in the implementation of minions?
I ask because I'm coming at this conversation from the opposite side -- I find their implementation to be pretty much spot-on.
WotC needed something easily disposable (for the reasons Jon Snow mentioned) but that remained a credible threat throughout a PCs's career. The simplest way of doing this is to give them a binary state -- alive or dead. Now, all this has been pointed out before, but I want to add something new:
Temporary Hit Points, miss damage -- the reason these things don't apply to minions is because they circumvent the entire reason for minions to exist in the first place. Making a level appropriate minion either harder to kill or easier to kill defeats the purpose for minions to exist. If they go down too easy, they aren't a credible threat. If they're too hard to take down, they ... well, they no longer serve their goal.
So, WotC gave us these minion rules (an admitted exception to the 4FS design you noted), and all they have to do is add two "sub-"rules to fix the problem, instead of making us do any clunky mathematics (div 4 HPs, for instance) or memorize a whole subset of rules.
Minions provide tactical variety with an absolute minimum of rules memorization.
They are... simple.
What could be more elegant?