The problem, really, is trust. Even if it were possible to build technologies that allow for law enforcement access (and something along the lines of mandatory key escrow might be doable, with a big enough bureaucracy,) there is no way that you'll convince me that our glorious leaders won't abuse that power.
Having spies spy on us in order to see if we've dark sided and are about to fly some planes into things? Okay, fine. But the instant they start using that capability to detect petty crimes (say, buying marijuana, copyright infringement for personal use, or grey market importation of goods) we're into a completely different world.
This is all of it - all of it - a question about the very principle of the presumption of innocence.
Our society only functions because - by and large - we ignore the petty, day-to-day crimes that we all commit. Each and every one of us breaks the law - knowingly or not - several times a day. If we could see every violation of every individual and chose to act on that, our entire way of life would collapse.
We couldn't reasonably prosecute everyone, several times a day. We couldn't expect people to live in fear all day every day that they might be fined or jailed for something they didn't even know was illegal. We cannot expect any citizen to know the totality of the laws in their own jurisdictions, let alone all jurisdictions they interact with digitally or physically.
How would we pay for it? Where does the money for those fines come from? The money for the lawyers, the judges, the jails?
This discussion is what is missing in this debate
Real world limits on the capabilities of spies. Limits on the sharing of information. Limits on what they will look for, what they will prosecute, how the information uncovered will be used. Real world consequences if those limits are worked around, loopholed or otherwise abused.
Maybe the ability to scan our communications is necessary in order to stop the Really Bad Things from happening. If this is the case, then before we even have a discussion about what compromises in technology we're willing to put up with in order to enable that, we need to have a VERY public discussion about how we're going to limit law enforcement use of those powers. FOREVER.