That's a very dangerous idea, because that's what we have done every other election, and look what it's gotten us.
Unfortunately just about every system of government produces this slide effect.
The Roman system of the emperor choosing his successor sometimes worked (produced the five good emperors in the 2nd century) but earlier you had Julius Caesar - who chose someone a little bit worse than himself (Augustus) who chose someone a little bit worse (Tiberius) who chose someone a little bit worse (well quite a bit worse Caligula).
Any system will be as bad as the people who operate it.
The NSA itself is not the problem to be avoided for your hypothetical. It's safe to assume that the technical capabilities of the NSA are the same everywhere. It's also fairly safe to assume that the "limitations" imposed on the NSA with regards to US citizens are about as effective as a cheese grater at holding water.
and the constraints on the NSA within the US are actually slightly weaker than those outside it.
Outside the US if they don't get caught they can do what they like. Inside the US if they don't get caught they can do what they like.
Outside of the US if they get caught they are immediately exposed and forced to stop.
Inside the US if they get caught they can use their considerable influence on the judicial system and the political system to keep it covered up - until someone like Snowden blows the gaff.
These "laws" will survive until the point where they are used against someone who has the intelligence and presence of mind to expose their inner contradictions. They are an example of the authori=ties refusing to face up to reality.
The compulsion to expose the driver of a car cannot survive the two possible drivers each claiming that the other was driving.
Similarly it is impossible to prove that you know something that you claim not to.
Also there are ways of securing an encrypted device that are not susceptible to forcing a single person to give up a password.
I would expect a competant intelligence agency to collect this kind of stuff. I would also expect a competant intelligence agency not to get caught.
By this measure the NSA is not a competant intelligence agency.
It has become sloppy because it has got used to using tame judges and politicians to cover up for its mistakes instead of avoiding making them in the first case. It has probably also become sloppy because it has grown to large and acquired too broad a brief.
This is a disaster because the NSA's incompetence has resulted in it being unable to fulfil its proper role.
By default the government has certain responsibilities - basically it is responsible for everything that we cannot do without. Where those responsibilities coincide with something that is a natural monopoly or where most providers will be "too big to be allowed to fail" (defence, law enforcement, finance) or something where market mechanisms cannot work properly (health, education, a safety net for the poor and the unfortunate) then direct state involvement is inevitable. For other necessities (eg food) the state will have to provide a degree of regulation and contingency planning. Any attempt to shrink the state beyond this inevitable (and rather large) size is a charade designed to enrich certain powerful individuals at the public expense.
Having said that there are some areas of the state I would like to shrink (because they don't fall into the categories above). The obvious example here is (so called) intellectual property.
this government, and especially the current administration, has proven that it can't run anything effectively.
Unfortunately the one thing that the government is even worse at than running something is procuring said something from a third party.
Once you add the fact that certain things are inevitably the responsibility of government then it becomes clear that the involvement of the private sector only makes things worse.
The key here is this - if something is essential then it is part of the government sector - even if it appears to be private - e.g. the banks.
The only way that helathcare can truly be private is if you regard it as non-essential - in which case the result is that the poor will die unnecessarily. That is a possible political position - but those who take it should admit it.