I guess a lot depends on what is meant by cheap or "emergency" and
2nd, "the more or less do what they are supposed to do".
The Hurricane was NOT cheap or an "emergency fighter". Yes it was cheaper than a Spitfire but aside from the airframe, everything else was identical. Same engine, prop, instruments, radio gear, etc. Overall cost of the fighter sitting on the field ready to go wasn't that much cheaper. The Miles M.20 was not only go around for Miles on this concept.
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The Miles M.24 which was basically a Miles Master trainer with 6 .303 guns in wing and the rear cockpit taken out and partially faired over. Used a 700hp (?) Kestrel engine. The RAF had hundreds of Kestrels in store from the biplanes of the 30s so no production needed. It was cheap, it just wasn't that good, speed might have been 250mph? Some accounts say 25 were converted on the production line.
One could argue it did what was intended (get 6 guns in the air at speed that might work for bomber interception? and not impact normal fighter production).
The Main problem with the He 162 was that it could not do what was intended. The actual performance was good. The actual intention was that they would be flown by teenage Hitler youth with basic glider training and maybe 30 hours of powered flight? Winkle Brown liked flying it very much, he also said it not an airplane for beginners. So did it do want was intended or not?