There's nothing broken about Marathon, it does exactly what it's supposed to. It's just requires a different approach when playing it, one which obviously you don't agree with. But that is only a matter of your opinion, and not a basis of fact. I can't say the same for Quick as I've never played that mode, but I suspect the same holds true. Just because you don't agree with the way a gamespeed changes the gameplay doesn't make it broken. It's just different.
No, definitely broken. Aside from the massively reduced unit cost (which arguably is just a gameplay change), you run into all kinds of scaling issues that were never addressed. Most per turn checks don't scale for mara (in fact those that do are the exception, not that I can think of any). This can create some fun issues, like:
AIs refusing to talk for 1/3 the time of normal
Guaranteed reactor meltdowns (though in mara's defense, reactor meltdowns are a total joke and should not be in this game)
Global warming. Oh my god, I doubt you've gone deep into the later ages after launching a lot of nukes. It's pretty bad on normal speed, but on marathon
every single land tile in the game will get hit. By a pretend effect that is better placed as a FFH spell than something to symbolize reality!
Tech costs scale. Tech costs given in peace deals for war success DO NOT SCALE. Therefore ironically on the speed that is by far the easiest to war, you can't get anything from peace deals, furthering incentive to keep going. Before you say this was intended, note that this works in reverse too.
Player spends a much reduced % of time in anarchy.
Per-turn checks like demands do not scale
Peace treaties do not scale (this really hurts quick)
Strategies that do not work at all on faster speeds will work on marathon. For example, the reduced cost and extreme speeds of warriors makes it possible to warrior rush on immortal with any civ in the game.
On the other hand, quick is bad for generally different reasons, but probably the most annoying is that high level AI bonuses allow it to 1/turn virtually every unit even BELOW deity, and suffers from reverse scaling options.
In a lot of senses, the different speeds are DIFFERENT GAMES OUTRIGHT, and that's fine. However, a lot of the things that do not scale appear to be or are flagrant oversights, and so while the difficulties are playable (even preferable in some senses), they are still broken.
Of course I do admit it's a little silly of me to single out game speeds in this context, SINCE EVEN IN PATCH 3.19 THE CONTROLS DO NOT COMPLETELY WORK IN THIS GAME. Maybe I should have just labeled them all broken and been done with it, but mara and quick have some unique offenses.
Edit: And yes, marathon is ~ to one difficulty less normally. Of course, unless you're at deity you can always play up
.