Yep, the NSA has been snooping on electronic messages and spying on citizens (including sitting US Sentators) since the 40s. All without judicial oversight and without any sign of real threats beyond criticism of the government, of course.
Changing policy while keeping the NSA around will just mean than the policy gets ignored. The NSA has already been smacked down once. Thanks to Snowden and others, it's now obvious that they've ignored the lessons they should have learned back in the 1970s. Heck, they're already doing an end-run around the President's just-issued "no spying on friendly leaders" instructions. The NSA is institutionally broken and their efforts are a net negative to national security. They're basically a rogue agency at this point.