2) It doesn't require all politicians to be be lack personal integrity and give way to blackmail, even a few can tip a balance.
3) Selective/distorted leaking could also tip the balance in places as to who gets elected.
4) Calls could be monitored to take advantage in negotiations for example by knowing what the real bottom line is in a negotiation, knowing which parts of a coalition can be picked off and exactly what they have been offered.
The question is not could the NSA take absolute control of all politicians but how many they would need to cause real corruption of the process. And I'm not saying that they are doing it now but that they shouldn't be allowed to get to a position where they could.
Regarding this in your disclaimer: "I am absolutely certain that there are enough politicians ready to mobilize to roll back NSA surveillance programs if they really think the programs are excessive in their scope."
Firstly there is no sign that they knew anything of the scope until Snowden, secondly "why aren't they doing it?" or failing that "if what we now know isn't excessive what would be?"
Disclaimer: Not a US resident or citizen.