> Should I also have no recourse when my house is burglarized if I fail to install cameras that send a feed to the police?
That comparison is wrong on multiple levels:
1) you may be automatically at fault already when not doing what the government is requiring you to do for public safety reasons (for example, your car has a rusty brake pipe, you do not do the yearly mandatory checkup, pipe explodes, car crashes into something)
2) contrary to a feed to the police, showing your federal ID card at a bank or car dealership when applying for a loan does not cause the government to know you were at the bank or the car dealership. Therefore it is not surveillance.