There’s nothing in mathematics that prevents key escrow, nor mandating encryption that has a master key. They might (or might not) be really bad ideas, but they are not inherently impossible.
Your key-under-the-mat analogy is helpful as today, if you don’t open the door for the FBI, or if you have died, the police, given a warrant, can open your door with force. They don’t need a key under the mat.
Yes, anyone else can open the door too, with sufficient force. That’s mitigated not by sophisticated doors (in most cases!) but by policing and legislation.
Similarly when you fly in the USA in a ‘plane, your luggage can only be locked by a padlock to which the USA government has a key. That’s already the case today. Of course, lots of other people have the keys too.
So it’s legislation that wins out in practice, and that’s agreed on as part of the political process.
Politics already trumps mathematics in society. If you don’t like the proposals to solve the problem identified as people hiding illegal activity in digital storage, either become part of the solution by showing why this does not need to be solved, or become part of the people coming up with a solution.