My experience: from untrained, kettlebell work (S&S specifically) got me from huffing and puffing walking up stairs, to barely a pulse rise and no elevated breathing for a regular waking pace.
You lost a good amount of weight since you began using KBs.
Put on a 20-30lbs weight vest and go up the stairs. I bet your pulse rises and you start to breath heavier again.
Just losing weight will make most things easier on the body which will result in lower HR during the same tasks. That doesn't mean that you improved cardiac function.
Look at it like this, compare how much fuel your car uses with just you in it compared to having your whole family of 5 in it.
It's the same car with the same engine, but it will have to work harder and use up more fuel.
The heart's the same.
Overweight and obese people walk around with constantly elevated HR, yet they usually don't have healthy hearts.
There's more to hearth health and cardiac function than just elevating your HR.
@MikeTheBear already explained this.
Using myself as a test subject I did not lose fat and already had huge amounts of muscle and neural coordination from hard style martial arts practice for 30 yrs. After doing S&S my 'cardiac' fitness improved dramatically, as in having an easier time doing the same things I did before. How is this possible without looking at the muscle pumping my blood around getting stronger? Not trying to argue and would sincerely like to understand the rationale.
See the things I wrote above.
IIRC you lost a good amount of weight, too. I think I read that you went from ~220lbs to 190lbs, back to 215lbs and back down to 190lbs again. Is that right?
"
having an easier time doing the same things I did before", that's exactly what I describe above. It could simply be by not carrying around so much weight.
I know that you're quite muscular. Muscle is a lot better than fat, because fat is simply dead weight while muscle is useful. Muscle is still weight though and for every pound of muscle you add your heart has to work harder, too.
The extreme examples of this are strongman like Eddie Hall, who was at risk of dying ins his sleep because of all the weight, despite a lot of that weight coming from muscle.
Another explanation could be overall stress.
In other threads you said that you trained in a variety of ways before. Maybe you trained so hard all the time that your stress levels were high. Than you switched to S&S and improved in many fields.
Sometimes less is more.
As an example, I'm a avid follower of Biathlon (cross-country sking + shooting) and a few years ago there were 3 or 4 women who came back from having babys. All of them tremendously improved and when asked how this could happen they said that because of their baby they couldn't spend so much time on training anymore and had to do less while focusing on the basics.
Maybe you experienced something like that aswell.
Or it was a combination of this and the weight loss. Who knows.
The point is there are many explanations for this and not just improved cardiac function.
Overall though I do think that swings improve cardiac function to a certain extent.
IMO the A+A protocols showed just that.
They can't replace steady-state work, but yield many of the same benefits. Will that be enough to count as "cardio"? Like many already said, that's up to you and how you define "cardio".
Why can swings improve cardiac function?
Here's my theory for this.
@MikeTheBear already explained the adaptions on left and right ventricule and why your HR rises during weight training etc.
I think swings play by slightly different rules. The HR increases during weight training stem from the restricted bloodflow which is a result of the contracting muscles.
This doesn't apply to traditional steady-state modalities like running, because the muscle contractions are so brief that they don't restrict blood flow.
Now if you look at the mechanics of a swing it's a hard brief muscle contraction followed by relaxation. That's not too different from running, rowing or cycling.
Your overall body tension is still higher though (think of the tension in the plank position), so you won't be as relaxed as you are during running.
IMO that's why you can have some of the same adaptions, but not all of them, but overall still can increase cardiac function.