Hi aalbert77.
Welcome to our Mattress Forum. 
You may be surprised to know that cool + soft mattresses are not as difficult to find as you might think, and don’t really contradict each other at all. All foam configurations can be as firm or firmer than innerspring mattresses/hybrids. As you mentioned, all foam configurations are less breathable and sleep a bit hotter than an innerspring model.
I’ve never heard of pocket coils being a culprit in the reduced air flow in a mattress. That’s an interesting piece of information. Where did you learn that?
To clarify, just the spring unit? Or the spring unit already encased in a mattress?
This, like much of what contributes to sleeping hot or cool on a mattress, is not something I can quantify as we are two people with different definitions of what hot/cool sleep on a mattress feels like and, of course, I haven’t slept on either of these units so I would be making pure assumptions. There is more about the many variables that can affect the sleeping temperature of a mattress or sleeping system in post #2 here that you may be interested in perusing.
Coils aren’t so much “soft” as they are “bouncy.” Coil gauge by itself wouldn’t be a reliable indicator of the firmness of the innerspring, although if all the other variables in two innersprings are identical such as coil number, coil shape, coil height, number of turns, coil diameter, coil arrangement, type of innerspring (linked or pocket coils), then a lower gauge innerspring with thicker wire will be firmer. The type and thickness of any padding above and below the innerspring and the specifics of the cover will also have a significant effect on how firm a mattress feels as well, and the innerspring is rarely the “weak link” within a mattress. You can read more about innersprings in this article here, and learn about the many variations and differences in the main types of innerspring units.
Different people can also have very different perceptions of firmness and softness compared to others as well and a mattress that feels firm for one person can feel like “medium” for someone else or even “soft” for someone else (or vice versa) depending on their body type, sleeping style, physiology, their frame of reference based on what they are used to, and their individual sensitivity and perceptions. There are also different types of firmness and softness that different people may be sensitive to that can affect how they “rate” a mattress as well (see post #15 here) so different people can also have very different opinions on how two mattresses compare in terms of firmness and some people may rate one mattress as being firmer than another and someone else may rate them the other way around. This is all relative and very subjective and is as much an art as a science. In other words … the only reliable way to know whether a mattress will be “firm enough” or “soft enough” for you will be based on your own careful testing or your own personal experience.
A cool, soft mattress could take the form of a latex + innerspring hybrid, or an innerspring mattress using other natural fibers in the comfort layer. If sleeping hot is something you wish to avoid, I’d suggest steering clear of polyfoams, memory foam (even gel foam), and synthetic materials both in the comfort layers and mattress cover/encasement.
I hope this helps.
NikkiTMU