It's not wrong to over-quote a shitty customer by an amount that'd make you willing to deal with their shittiness. That's totally fine on your part actually, since either they take the bid and you make money, or they don't and you don't have to deal with them.
The only way I can increase prices is if I stop having an advertised price and go to a pure ‘contact us for pricing’ model. I can either be mass market at commodity prices or I can target governments at inflated costs but I can’t do both. We’re the last hold out in my niche and eventually we will have to leave the commodity market.
The typical strategy is to not ask for clarification and use deficiencies in the spec to justify change requests that gouge them. You need a cadre of lawyers to be able to play that game though.
Also there are a million of different governments and all different levels, I’m giving one anecdote as it applies to one of them. I’m sure many others have a different experience.