As a very overweight rider who doesn't do enough miles ..... I have to agree it is not just leg strength. I have done group rides where I could barely manage the hills---as in, lowest gear, struggling to keep moving forward---but could easily match the group's speed on the flats.
Yes, my legs are weak, but also, muscles need fuel and air ... all of which is delivered by the bloodstream. Heart and lungs are really important when climbing. Under constant load your muscles need to offload all the waste matter while also sucking in all the oxygen and fuel they can get .... and if you cannot breathe hard enough and pump enough blood, your legs muscles cannot contract no matter how strong they are under optimal circumstances.
If you really want to get good at hills, I would suggest intervals and hill repeats---which are intervals uphill. sort of.
Easiest are the intervals .... basically, ride flat-out for 30 seconds, rest 30 seconds, over and over .... ride until you want to quit, then until you need to quit, then until you are about to fall over. It has been explained to me that intensity is what really matters ... . do fewer repetitions but go Really hard for each one .... then finish a normal ride to clear out your muscles.
If I were going to ride intervals I wouldn't do what I just suggested, though ... I would go online and look up "riding intervals" and "HIIT" (high-intensity interval training.) Learn from the experts, because I am Not an expert.
Hill repeats are just that .... find a hill, attack it, roll back down, do it again, and keep doing it until you can barely do it .... then finish your ride to clear out your muscles.
There are a lot of training programs online ....
Anyway .... yes, lower gearing and better technique matter, but those aren't the "Answer." I have been practicing breathing technique (make sure to Fully empty your lungs--panting is inefficient and exhausting) but I still need to practice intervals and hill-repeats .... the heart-lung machine is extremely important in climbing.