The battering ram isn't really the right analogy. It's not a matter of them having particular equipment, or techniques, which they can legitimately use as part of their job. And it's not like they are very visibly damaging lots of things.
This is more like a society in which the police routinely break into houses by picking the lock in order to rifle through your papers secretly, without telling you. They say that they have secret warrants to do this, but since they're secret, and they do the breaking in in secret, you can't even find out if they have broken into your house.
People don't like this; they don't like the idea that some cop may be in their home rifling through their things. So they start developing stronger and stronger locks. The police get worried that they won't be able to pick the locks on your doors, and will actually have to get a warrant and not break in secretly. So they lobby to pass a law that all locks have to either be weak enough to be picked, or have a master key that the police have. Of course, the people, who don't like the police breaking in with impunity, defeat this bill.
So the police don't stop there. Instead, they just make secret deals with a few key lockmakers, to build locks that accept master keys anyhow. When lockmakers standardize on key designs that are more secure, the police add a section to the standard that makes it so that any lock that implements that standard will be able to be opened with a particular master key, but in a way that you can't tell what that master key is from the standard. Since there are enough lockmakers that they can't subvert them all, and not everyone implements those standards they subverted, they also talk to a few doormakers to add a secret part that you can push to disengage the hinges.
Now this information comes out. People are outraged; their lockmakers are supposed to make locks that even the police can't get in through; people don't trust these secret warrants and secret searches, and with good reason, as the police have used these secret searches to investigate ex-lovers before, not just terrorists. They're outraged by the betrayal of the police, making an end-run around the law that they thoroughly defeated to prevent the police from having master keys. They're outraged by the lockmakers subverting their trust.
And what's the police response? "We need these tools to investigate terrorists and criminals." Never mind that in order to investigate terrorists and criminals, they've weakened everyone's security, and everyone's trust in their government and the companies that sold the compromised locks. Never mind that they've been through the houses of many innocent people, in a wide sweep to try to find evidence of a few criminals. Never mind that the system has been abused many times, but the only way the abuses have come to light is by whistleblowers who the police prosecute severely.
The police (or the NSA, to step back from the analogy to the real world) find these tools useful in their job. I'm sure they do. But the public finds these tools too intrusive. I'm sure it would be useful for the police to be able to secretly break into any house they wanted, rifle through people's papers, and find people who had jihadist leanings that way. We have amendments in our constitution specifically forbidding that, for good reason.
Likewise, regardless of how useful the NSA finds these abilities, we the public find them abhorrent. Just like the police should have ways to get warrants and under the authority of those warrants, search houses, there are definitely legitimate uses for some of what the NSA does, if properly regulated. But weakening everyone's security, so they can intercept and read your mail at will, in secret, with no oversight, is just as wrong as the police breaking into your house in secret, at night, and rifling through your belongings.