I answer late because one point in the first post was overseen as it seems.
Every mission I send a soldier with a stun rod and every mission he just gets killed. Aliens don't like to be touched and react violently when you approach. Also I lose a lot of soldiers trying to keep a alien alive while my stun rod soldier is trying to get into position to do his thing.
Aliens won't react if they have spent most of their TUs. If you stick to the rod, make them react before the melee attack (I precise this point because it's the same if you have to send someone in the open and you now several enemies have a LOS on him).
The few times I used the stunning rod, I tried and wounded the target with small arms (or a grenade for Ortnoks), but only in the last turns, so that all the team could be affected at this task, and attacked it with two soldiers with TUs to be sure to knock it down (after reaction fire phase was over).
That being said, the autopsies->live alien->alien mind etc research tree is way overestimated. It is of very little tactical value in the campaign, aside from the gas grenades, but these alone are insufficient to justify investing so much research time. The memo you get about that it's important to capture live aliens is wrong, as of current development at least.
So true, and I'd say it's clearly a left-aside topic in the current development. I mean, while the Alien Mind research tree is not done. Seeing as the X-Com live aliens management was far more involved, and guessing that this implementation would mean more code and research handling (For example, there are no ranks nor functions among the Aliens, only different mission teams.), I understand this. But wouldn't have a higher required number of prisoners (and a more varied composition between species) been simply feasible, while the research tree is still in WIP? Currently, as you said, neither stun rods nor stun grenades are mandatory to reach this number.
If the number was higher, perhaps, stunning rods would become an option (even with the same research incomes, for the present).
Stun grenades keep being useful (until you reach interesting reaction stats) to help fending ambushes off from unarmored Shevaar, though.
In my opinion, a dedicated base would be needed to thoroughly study live aliens (as back to X-Com).