You're right about the relationship between A of A and airspeed, and the relationship between airspeed and glide distance, but it's really not about
rate of descent so much as glide ratio (horizontal distance for a given vertical distance).
If you look at the POH, you may see a glide ratio noted... this is the ratio you get at Vbg at max gross.
Unless you are stalled or slipping, going slower is not going to make your vertical speed greater; in fact you should descend more slowly, up to a point (your minimum-sink airspeed). But it may
shorten the distance you can cover, if it is below the appropriate best-glide speed for that weight.
And because all V-speeds increase with weight, the only thing different about a glide at low weight vs. high weight, assuming you have nailed the right best-glide airspeed for your weight, is the
time it will take for you to reach the touchdown target. You'll be going forward faster or slower and descending faster or slower, but the ratio of height/distance will stay the same.
It is true that in a normal final approach in a 172, with flaps out, you may well be flying below Vbg, so you may descend faster, and slipping will also slow you way down and make your vertical speed increase. Vbg is not vital when the engine is working, so flying below the actual Vbg for your weight, with that "elevator going down" effect, is normal.
But in an engine-out scenario, you will have to fly at Vbg, or you just won't get the most distance for every foot of altitude lost. Obviously, sometimes you want to steepen the approach, like when you have to get over obstacles onto a short runway or emergency-landing site, but when you are looking to get the most mileage for your altitude without using power, Vbg, and no slower or faster, is the secret. Even if Vbg for your plane is 300 kts, you won't go any
farther if you go at 310 kts. You'll come up short, and get there faster.
To descend as
slowly as possible, you need to fly at minimum-sink speed, which is a little slower than Vbg, and again, dependent on weight. But if you go any slower or faster than that, you will descend more rapidly. In fact, you won't have to slow down much at all from min-sink speed before you stall the wing, in which case you will descend
very rapidly!
You can look all this up, or trust a pilot whose last few hundred approaches and landings were made without power. And I wouldn't have gotten my PP-G or the commercial rating if I couldn't roll to a stop within 200 feet of a pre-determined target, without rolling past that target.
But you obviously get the important idea: that you usually won't get the desired result by simply pointing the nose at some point on the ground.