My own head-canon is that what we think of as a "heat sink" in-game, really isn't any one type of thing. A heat sink isn't a big air conditioning unit that is built into the mech. A person in-universe wouldn't say "my mech has 15 heat sinks" just like they wouldn't say "my gauss rifle does 15 points of damage". It's a game term that would be translated into a significantly different form. (Note: there very well might be some statement somewhere in one of the books where a character says exactly that, but if there is, I think it's bad writing).
Instead, a "heat sink" is a set of construction techniques and materials that are known to dissipate heat. These get abstracted into 1 ton, 1 critical components for gameplay, but that's not how a character in-universe would think of them. Critical damage in the game would represent smashing something that was important, and now the mech doesn't cool quite as well. So, you're going to have cooling lines that run through the mech. You're going to have cooling jackets around the weapons, exhaust ports that get rid of superheat gases, surface area, specialized metals that better resist the effects of higher internal temperatures, etc. Everything from where ammo is stored, to how your myomer bundles are wrapped around your weapon housings.
"Double heat sinks" or "Freezers" are a slang term for advanced Star League construction techniques that radically reduce heat. It's a bulkier system, and it really limits weapon placement within the mech (you can't cram things together as tightly). This is represented by the higher number of crits they take up. But it's not like a super air-conditioner, it's a variety of advanced heat management systems within the mech.
This would be why mechs (originally, I don't know about how it is now with all the optional rules) can't mix and match double and single heat sinks. It isn't like plugging in a new AC unit -- you've got to make significant changes to the internal layout of the whole thing.
Vehicles can't use them because these advanced construction techniques just aren't used in vehicles, for whatever reason. A vehicle's traditional "heat sinks" would be very different in design from a mech's. Improved myomer shielding doesn't really help a vehicle that doesn't use myomers.