What's your background? That's incredibly limited way of looking at things. You posted a few studies in regards to geriatric (elderly) patients and OA (osteoathritis), which I guess you didn't read. This is from the first study you posted:
"The authors stated in the text that their original intent had been to have people exercising at an intensity of 80% of 1repetition maximum (1RM), but they found in pilot testing that 7/10 subjects were unable to complete the exercises at this intensity because of pain. Therefore, high intensity training was conducted at 60% of 1RM with 3 sets of 8 repetitions and low intensity training was set at 10% 1RM with 10 sets of 15 repetitions. After 8 weeks of training, both exercise groups had significantly reduced pain and improved function compared to the control group, but there were no significant differences in these outcomes between the high and low intensity training groups. No adverse events were reported."
I work with this patient group on the daily atm and it's not as simple as you make it out to be. While progressive overload is definitely the way to go, it's not heavy in the sense that you think heavy is. Also, trust me, the majority of elderly patients, especially with new hips and knees, cannot squat with a barbell. You have to work from a completely lower level. Some of them can't event move their limbs against gravity and wont achieve full ROM (bone spurs, alloplastic, metal). You work with what you have and improve what you can and that takes a lot of work.
The second study you posted is post stroke patients and yes they used 80% RM, which is fine, but they used leg extension machines and leg curls, no squats. Another important thing is that the control group did nothing at all.
The third one was not based on RM, but rather 30-40-50kg of 11 reps for 3 sets in a leg press and leg extension machine. The patient group was hemiplegic stroke victims, who improved their isokinetic strength (obviously) and got a slight increase in stride and 10-m walk test. There wasn't even a control group. Surely hemiplegics will improve after a stroke with a lot of different exercises programs.
The first article lists reasons like "you'll get toned" and "you'll feel confident", and while it does advocate lifting very heavy when it goes into something "scientific" (it doesn't reference the study and one study is barely anything) it also has this to say:
"Results of a second power workout that used light weights (30 percent of the 1RM) and explosive movements found that higher threshold of motor units were recruited earlier in the movement (....) Doing jump squats, Olympic lifts, or plyometric push-ups stimulates the brain and corresponding motor units more than slow speed squats, overhead presses, or even push ups even if they are trained to failure" And it then talks about using different training modalities.
I'm not going to go through more of the articles. Everyone who gave you a pat on the back hasn't read them or the studies, and neither have you. There is no doubt that progressive overload and strength training is something everyone should do one way or the other, and that squatting is one of the best exercises, but claiming that "just squat, and squat heavy" is somehow the most important thing in the world and improves all health parameters is straight up bullshit. Having good form, keeping pain free, using progressive overload over time, keeping active and finding the right exercise choices matters more. If there's no reason for you not to squat very heavy, and that's your goal, then you defintely should do it.
As for the TS: Yeah just start working out your lower body. Squat variations, deadlift varations, lunge variations, leg curls, leg press, BW stuff are all good choices. Work on form and keep loading more over time. Keep it around the 70-90% range for the compounds when you get it down. There's plenty of good exercise templates out there for the lower body.