But when the FBI gets the key or picks the lock it does not make any other door more insecure, or enables other parties to get into other doors.
What if the FBI would ask all landlords to install a special door to every apartment, but only the FBI has the key to this special door? What if someone successfully copies that key? Now they have access to all apartments.
First off, this already happens: every major corporation uses multi-party disk encryption, usually branded as "recovery options" or some such. They keep their private keys secure.
Second off, the FBI is not asking for a special door to every apartment. They are asking a lock manufacturer to create a key and use it to unlock a single lock that is brought to them, after the lock manufacturer explicitly designed their locks to make the creation of such a key possible, so that this legal case would exist.
There is an interesting debate to be had here, but this rhetoric using overly simplified analogies is not it.
Obviously, "making all locks insecure" is a different situation than bypassing a single door. Which is why we don't do the former, but (currently) do the latter, judiciously.
But hey: what if the lock company makes a standard lock, with a plain ol', low-security, five-pin key, and attaches it to a bomb that destroys the apartment when it's picked incorrectly? Does the lock company now get to beg off when the police come looking for help opening a single door?
"Oh, we'd love to help you, officer, but you see...if we help you open this particular lock, then all criminals will know that you can disable the bomb, and that would make all of our locks less secure!"
What if the FBI would ask all landlords to install a special door to every apartment, but only the FBI has the key to this special door? What if someone successfully copies that key? Now they have access to all apartments.