One problem (among many) is there's no such thing as "the" government. It's a relative term and its meaning depends on context.

If we take it to mean all governments, then that means China gets a copy of the key and can use it to spy on the communications of the Australian government.

If we take it to mean just one government (or a few select governments), then what is the criteria for deciding the government of country X should have a key but country Y should not?

Ultimately of course it comes down to a matter of coercive power and jurisdiction, which particularly complicates efforts trying to build products or services that are intended for global usage. I believe we need to push back against anti-encryption laws in the west so we have some ground to stand on when making a case that they shouldn't be accepted elsewhere.