I think the techincal issue is guaranteeing the that the backdoor, whatever form it takes, can only be used in the service of a lawful court order.
At the end of the day backdooring encryption does nothing but weaken everyone's security without actually helping intelligence agencies, at least in the face of serious actors.
Fine, agree to a global backdoor or all crypto with a handful of trusted key holders, how long until the algo or key is leaked, how long until a flaw in it's implementation is found, how long until some TSA agent is photographed with the password blinking on his screen in a news article.
All this will do for bad actors is ensure they assume whatever service provider isn't to be trusted in their implementation and just use a 3rd party process and/or open source tool chain to produce encrypted messages that will be routed over already encrypted networks. Great, your backdoor got you to a second layer of ciphertext that you still can't make heads or tails of, meanwhile you've weakened the security of literally every person on earth.
A backdoor is unacceptable, no matter it's perceived strength, value, or safety.
The problem here is not a technical one; we don't between a "safe backdoor key holder" can really exist.
That would be the just-world fallacy.