I'm not disputing that Queens can be used successfully against Mech, I just don't think your analysis shows why it works. The resource cost of the queens in isolation doesn't matter that much, you have to see it as part of a larger whole.
Look at Jaedong's game against Flash on Destination this year (sorry I'm at work and don't have the link handy). If I remember it correctly he lost quite a few queens before they could kill a tank, and he used them all just for one break, it wasn't a continuous sapping at all. So if you analyze the resource cost of the queens vs the tanks it wasn't that good, maybe even negative, and that's not even counting indirect costs like the attention to use them or how you have to pay for them way in advance and then sit around doing nothing while they build energy.
But he still won the game, because the queens did *enough* damage that his hydras/lings could break through the remaining mech. If the queen money was spent on extra ground units or mutas, it probably would have failed, because it's just so ridiculously hard to break through a large and well-positioned mech army. And you have to break it all at once, not just pick off stray units because otherwise they'll soon be sieging up outside your expansions and you lose.
I see what you're saying. The way I look at the situation is idealized, I admit. There are no guarantees a Zerg player can use Spawn Broodling before a Queen gets killed, so they aren't as valuable as I make them seem. What I can say is that if a Zerg player can keep the Queens alive and consistently get shots off on the expensive Mech units, it is good for him. If it's too hard for him to use Queens and he can't help but lose them to Turret fire or whatever, then they're less than useless and shouldn't be made.
u could also look the eng upg like this:
assume each queen casts 1 broodling before dying
assume you have enough time to upgrade energy before making queens
assume the 15 seconds extra regen time for +12.5 energy is negligible
1 queen 1 broodling takes 100 energy (for first cast) and costs 100/100
thus each point of energy costs 1/1
eng upgrade costs 150/150
thus it needs to provide 150 points of energy to break even on cost
eng upgrade provides 12.5 energy
thus you need to build 12 queens after eng upgrade to break even
if you adjust the assumptions (1.5 or 2 casts per queen, add a time constraint etc) it tends to look worse for the energy upgrade
you can do the same thing for all the other energy upgrades, they all suck for the most part unless they provide more utility (plague and swarm on one defiler for example)
Buy 12 Queens and get 1 Spawn Broodling spell for free. I think that's a great way to think about how the Queen Energy upgrade works. Honestly it isn't really worth it unless going mass Queens in the super lategame is a legit strategy.
There is a useful energy upgrade actually, and that is the energy upgrade for the High Templar in PvZ. Since Psionic Storm costs 75 energy and each High Templar spawns with 12 more energy, you basically get 1 free Storm for every 6 High Templar you build. The energy upgrade is useful once you can start mass-producing them.
Next experiment: Is ensnaring mineral lines worth it?
HAHAHA, that's tempting.