If you have some bug overpopulation problem, usually that is one or two specie. Then the best thing is to address these selectively, e.g. spreading their predators around in the right moments (usually in the early larval stage - like mosquitoes are eaten by frogs or many fishes,...). That uses to be way more efficient than all traps, killers or so.
Or keep the many birds in your area happy - they will consume even the adult insects and in very large area...

But what if the problem is for most/all species of insects in the area?

But what if the problem is for most/all species of insects in the area?

This I do not believe at all.
You mean all the butterflies, moths, bees,... as well?
There may be 10's of varmint species around you, but 100's of other's just either "inert" for you and/or even the good ones (those, who actually hunt and eat the varmint ones or their larval forms,...).
It may seem to help for the day, but it may well make the thing way worse the week after...

Actually the outdoor zappers have worked wonderfully for me in the past in keeping things to a manageable level.  Sure the bugs always come back, but while it is on and I am outside at night, there have been much less bugs to contend with.  Now that I live in a dry climate, I don't have to worry about them so much. 

Actually the outdoor zappers have worked wonderfully for me in the past in keeping things to a manageable level.  Sure the bugs always come back, but while it is on and I am outside at night, there have been much less bugs to contend with.  Now that I live in a dry climate, I don't have to worry about them so much. 

Here, the city apparently sprays insecticide to get rid of mosquitoes. But the bug zapper catches other bugs, like moths or gnats.