Consider Tabata protocol.
It is supermaximal effort protocol, participants are required to exert maximum effort repeatedly.
The duration of active phase of Tabata is 20 seconds, half of approximately 40 seconds after which maximum performance (power output) drops significantly, because body switches to a different energy system.
In my experience, Tabata squats are done in range of 16-21 per 20 seconds of active phase. So, basically, Tabata squats are equal to somewhat less than 8 sets of 16-20 repetitions done close to failure. The failure usually come after first active phase, so that's why there are "somewhat less than 8 sets." I personally define failure as breakage of exercise form or exercise pace, and this is what I and others experience in Tabata squats.
And you know what? If you go close to failure, muscle mass and strength grow in the range of 5 to 35 repetitions [1].
[1] https://www.youtube.com/watch?v=dN_c4sQwfTI
PS
Other HIIT protocols are similar. For example, 3 one-minute-active-phase-one-minute-rest supermaximal protocol also leans close to "3 sets of 35 repetitions done to failure" - squats' pace noticeably quickly deteriorate to 1 squat in two seconds.
In my personal experience I've found strength training better for losing weight than just cardio but any activity will help a bit. You'll really need to adjust your diet in some way for it though, or at least start counting and keep your calories steady as you do more activity. Trying to outburn what you eat takes like an hour of exercise a day otherwise, it's tough.
The problem with doing a lot of cardio is that you need muscle to burn calories (especially so without injury and as you get older), and too much medium intensity cardio will start to chew up lean mass.
No harm in doing a bit of both though, especially if your goal is fitness/maintenance rather than maximum strength or a particular look.
Tabata (the sprint/recover running technique) was developed, I believe, to increase VO2-max. It should help with overall endurance, and you can go on a long run each week. That would probably be efficient.
I guess the answer for optimizing time is to get a home treadmill if removing the commute to a trail/track will make the timing work.
But it's not, unless there is a calorie deficit.
If you do aerobic exercise, almost all the energy comes from burning fat. Because your body will have used very little glucose, you're unlikely to feel particularly hungry after that exercise.
If you do anaerobic exercise, almost all the energy comes from glycogen stores. Your body will crave carbohydrates immediately after exercise, and only resort to glucogenesis burning fat if you don't fuel enough afterwards.
There's a significantly higher risk of over-consumption after doing anerobic exercise and aerobic exercise because your body wants to replace the glycogen that got used up.
Both forms of exercise are shown to have an "anti-hunger" effect.
And unless you are walking, your body is also shunting blood away from your gut which also has a secondary hunger dampening effect as it doesn't resume blood flow too it immediately.
So for anything we would call aerobic exercise, that is zone 2 "cardio" or greater, I would have to disagree with your main claims about it.
For aerobic exercise, your body gets around 95% of the energy from burning fat. If you are doing exercise where you are 50/50, then it is by definition no longer aerobic exercise but anaerobic.
Anaerobic exercise starts at the point that your body is forced to use glucose from glycogen to provide energy because you have reached the limit of the energy your body can produce from burning fat, because your body can't provide oxygen at the rate required to do so.
Everything from minimal activity far below VT1 to VT2 (a.k.a. "lactate threshold", LT, a.k.a. "anaerobic threshold", AT) is "aerobic".
Near the VT2 limit, very little fat is used compared to glucose. Fat burning proportions as high as 95% are only reached under very light activity. (And/or in glycogen depleted exercisers whose body has switched to fat out of necessity). That doesn't represent the entire aerobic range.
There is aerobic use of glucose (below the lactate threshold, "clean burning") and anaerobic (above AT, generating lactic acid).
A useful parameter is the absolute fat burn rate. Maximal fat burning does not occur at exercise intensities that derive a large proportion of energy from fat. Supposedly, this "FatMax" exercise intensity fairly closely coincides with the VT1 threshold. Here, around 60% of the energy comes from fat.
I'm "fat checking" all this as I type; I used to know more about this stuff, but forgot a lot.
At LT1 (via lactate measurements) at peak 100k fitness with elite economy (n=1) ratios were roughly 23% fat, 77% carb. FATMAX was near 28% at slower speed. This is via training using the now-standard (at elite levels), high-carb approach for fueling ultra marathons.
So many factors--including gut training and fueling--play into this. Most aren't even aware of the details, and the "we don't need no carbs for performance" folks still generally bury their heads in the sand. For performance, we're seeing huge skews to carb-based energy for endurance that were considered "wild" just 5 years ago.
https://knowledgeiswatt.substack.com/p/20-120-vs-90-gh-of-ca...
I thought it would help illustrate what you're saying but, gosh, those Y axes aren't making things easy to interpret. For those willing to do the mental arithmetic, 1g of FAT is 9 kcal and 1g of CHO is 4 kcal. :)
P.S. It also only starts at 150W.
"anerobic exercise and aerobic exercise" should have read "anerobic exercise compared to anaerobic exercise".
but bigger reason imho is that people overestimate calorie burn from exercises and fool themselves into thinking now it's OK to consume more food.