As an old-school DM, I'm against all of the above. Every single one of these could be advocated on the fly by a clever DM, thus, there's no real reason for absolute rules.
Fair enough, though you do reference skill checks and challenges more than old school DMs usually do.
I mean, a chase could be a single opposed check, a series of skill check from the PC (whichever side he's on) or a skill challenge-like thing (first of the 2 participants that gets X checks ahead of the other, you can take a roll to try and give negatives to the opponents next roll). More likely, I'd use all three in different situations, it all depends on how important the chase is.
The same could be said of any conflict in the game. Mass combat could come down to a single check, a BD&D Battlesystem approach, or all out tactical minis boardgame.
I assumed it went without saying that I was referring to a more involved level of rules. You might wing a chase just fine, but there might be a clearer, more engaging, and consistent way of doing it. Maybe it faintly echoes a skill challenge maybe not, maybe it uses a map in a new way. But you would have the option of zooming in on a dramatic chase scene with rules support to allow tactical decision making.
Plenty of games have such rules, Hot Pursuit was a very popular supplement, and there was a recent Unearthed Arcana article called "Fight or Flight."
And for fighting on top of a giant monster, well, balance check every now and then to see if folks fall off (give them a few saves if they fail, they are either on the ground, holding themselves above nothingness on a monster spine, or dead on the ground) and whenever the DM thinks about it, the giant monster tries to swat an area on the battlefield.
Since second edition there have been special rules unique to certain classes/kits which detailed this sort of thing. IME it's not a fringe scenario, maybe in yours it is.
My point is about complex fights which, say, take entirely on the back of a flying dragon. Sure this might be run as a skill challenge in 4e terms, but I don't think skill challenges RAW do this sort of scenario justice. I mean what happens at 3 failures, the entire party falls to their death?
In short, rules are not needed in my opinion for things I can easily pull out of my nethers, it takes up precious space in the book and makes actually doing the thing often about shuffling in rulebooks to find the exact rule for the situation.
You may be content with a 30 page rulebook, and that's fine there are plent of rules light games that go for an old school feel that do this. But to claim D&D is or has been one of them is just not accurate.