Few answers to that Mike:
1) The quicker you recover, the quicker you will get stronger. If you can train, recover and go again stronger in half the time the next guy takes you will be stronger quicker. To enable you to do that there a multitude of factors involved, some of them we can change, some we can't:
- Genetics: Not much we can do here.
- R&R: Sure there is plenty we can do to get more rest and recuperation, but in the grand scheme of things and compared to our ancestors physical over-exertion is hardly the scourge of most modern people.
- Eat better: Again a lack of food is hardly the scourge of the modern man.
- Stretching: Enabling better form through dedicated stretching. This is something which ranges from "yeah I should do more" to "no it's useless" which really is a shame. Dedicated stretching can transform your squat from looking awful to looking passable or better.
- Specific strengthening: Related to the previous point, specific strengthening exercises to enable better form. For example specific thoracic work can really help people who Squat bent over.
- Practice: Related to what you said, practice, practice, practice helps and allows for active recovery.
The first few points there you can't do much about and/or are largely taken care of but what about the last few? Are they honestly been given full attention from the "eat more and squat" crowd? I rarely find that's the case. Going to the gym is fun, sure it's fun to pretend we're the cast members of 300 and/or Vikings and/or it's a life or death battle against the iron (whatever the hell that means) but let's remember it's probably the least stressful event of our day. Training is the easy part, stuffing your face afterwards is the easy part but the rest is harder, much harder and it could be what separates a 400lbs Squat from a 550-600lbs one.
So yeah Mike, there are plenty of things you can do to enable you to Squat more frequently and squatting more frequently *as long as you recover* will speed up your gains.
2) On a related note, the reason pulls are generally not trained as often as Squats is that 'in my opinion' the strongest position for the Squat is relatively safe and natural for the human body which is why load is distributed evenly and recovery happens faster. Therefore frequent Squats are usually productive as long as the person can Squat to at least a decent standard. This is also the reason that Benches can be performed frequently by those who can actually Bench safely and have put time into making it a safe lift for them (strengthening the back, lats, traps. Stretching the shoulders etc)
On the flip side the strongest position for a Deadlift is usually one which involves a slow grind with a compromised back position. So the alternative and one which people have picked up on is to use variations of the Deadlift, usually short range (partials) or arch-specific (RDLs/GMs/Dimels) with the addition of some heavy, grinding round back (SLDL/Deficit) pulls thrown in there.
3) Regarding volume. Everyone needs to put in some serious volume *at some point*. I think that's the main reason for stagnation amongst trainees who have started off with high volume routines and moved to low volume route. They move to low volume and reap the benefits of increased strength as they are effectively *peaking* but they stagnate and usually then blame genetics or any other number of factors (anything but actually finding a solution, God forbid we start actively search for something different).
Cycling through periods of high volume/frequency and low volume/frequency is usually the best solution. It is the contrast which forces growth. That is the reason behind the 2 week heavy 1 week deload that I use.
You can look up 'Elevating the Pyramid' by Bill Starr which I've posted in the articles section for more details on this building up of volume.