[Pseudoscience-is-malarkey (OP)]

Also, should we never kill a bee nest? They're so valuable to our ecology and are not very aggressive- and when they do sting, they don't hurt that much.

[alancalverd]

I've watched professionals (the French fire brigade) deal with hornets. IIRC they started with smoke to calm the beasts down, then injected a poisonous powder. But the key element in the process is the white space suit worn by the operators - you don't want to get grumpy hornets or even slightly dozy ones inside your civilian clothes, or breathe the nerve agent. 

If you have a nest of honey bees, it's worth talking to an apiarist - they are valuable and worth a bit of care and protection.

[Colin2B]

I've watched professionals (the French fire brigade) deal with hornets.

I think these would be Asian Hornets, an invasive species which has caused havoc to bees in France. Very aggressive, an average of 5 French farmers are killed each year trying to deal with their nests. The special suits are necessary as they can sting through a standard bee suit and they can spray venom through the mesh hood. Tactic appears to be to blind the victim and then sting to death.
Here they are a notifiable pest and teams are brought in to locate and destroy the nests.
Interestingly, one technique to locate the nest is by catching a forager and putting a tiny transponder on it!
Our native European Hornet is relatively harmless and shouldn’t be destroyed.

Also, should we never kill a bee nest?

Only done as a last resort with a diseased hive which has one of the highly infectious, notifiable diseases.

[Petrochemicals]

Bag the nest, cut it down and spray insecticide in. Leave for 24 hours. That is how wasp nests in the UK are dealt with.

[vhfpmr]

I bought a spray can in Tesco for killing wasps nests. It squirts a jet about 8-10 feet, so you can drench the nest from a safe distance, then you just leave it a day to soak in before cutting it down and chucking it in the bin. I ignored the instructions to do it at night whilst they're all at home, so I had to do it all again after they came home to find their first nest uninhabitable and set up home again in a nearby hedge.

My father once picked a bees nest up and chucked it on the compost heap thinking it was a clump of dead grass.