You are correct that we can engineer a cryptosystem with two sets of keys.
However, nothing prevents keys from being stolen by someone else. In a normal cryptosystem the security of the key is entirely up to you; but in a "law enforcement accessible" system now you have to worry about the feds getting hacked, too. And since the feds will have backdoor keys for many, many users; there is much more interest in stealing those keys.
Physical security has a different set of tradeoffs. Notably, you have to actually be physically present to manipulate and defeat a physical lock, which is what I was alluding to. Even then, it provides an example of how easily a backdoor can be compromised. The Travel Sentry system exists to allow TSA employees to unlock and inspect luggage. There are seven master keys in total; copies of which are spread around thousands of airports with tens to hundreds of TSA employees each. Suffice it to say, the master keys leaked decades ago and you can buy them off Amazon for a few bucks. Any such backdoor key will need similar levels of access to government employees and will likely leak for the same reasons as the TSA keys. Except that the consequence of an encryption backdoor key leaking will be much higher than someone being able to open luggage locks.
Politically, there is also an argument that we should be able to keep secrets from the state. Certainly, there is a reason why we have a 4th Amendment, and it is not because searches and seizures just so happen to be inconvenient.
As for age-of-consent checking, the problem is that existing age verification services would be able to track everyone who accesses an age-verified site. Which, given today's legal climate basically demanding age verification for everything[0], would give the verifier access to your whole browsing history.
Physical age verification is relatively privacy-preserving: I present my ID and that's that. The government that issued that ID does not learn where I presented it, because it's an offline credential. The people I'm doing business with do learn my identity, and they could sell that information, but that's something they didn't need an ID to do (so we should pass a law to prohibit that).
[0] There is also a political argument that the 1st Amendment precludes age verification on social media - aka "don't censor kids"