How reliable is this concept in general?
Theoretically, it is reliable. The only risks are as follows:
a) resurfacing due to not weighing oneself down sufficiently or weights becoming detached
b) someone seeing you before you are submerged
c) regaining consciousness underwater (e.g., if there is laryngospasm) and somehow being lucid enough to resurface before passing out again
d) convulsions causing one to flip over (applicable only in shallow water)
The way I see it, it's a tradeoff because doing it in a lake one has to contend with a, b, and c, and doing it in a bathtub one has to contend with c and d.
In regards to inhaling gas to pass out in front of some water, then once you fall and sink into the water immediately, you will just drown peacefully and not wake up again, due to lack of new oxygen being inhaled?
If I were doing it in a lake (as I still might), I would probably inhale it until I felt dizzy, then submerge my head. Most likely one would not regain consciousness, but because of the vasodilatory response and sources of variance between individuals such as lung capacity, it's possible that consciousness could be regained briefly. That being said, obviously it would occur relatively soon after LOC, making (IMO) permanent organ damage unlikely.
Because I'm thinking if it was indeed so simple and reliable, how come this method isn't more popular and common
I doubt that's the best heuristic because people use all sorts of unreliable methods and forego more reliable ones. I think it's simply not well known.