Really? How?
If you want to enable communication where both parties don't need to be online at the same time, and with easy setup of a trusted system, you will need something very much like the signal protocol.
That requires setting up a pretty complicated central service. Moreover, you are going to need to do quite some updating on the end-points of the e2e encrypted communications? Setting up this kind of operation, when illegal to do so, is hard. Moreover, it requires certain expertise that is not common among criminals.
How many criminals are going to be able to run this correctly? How many of these systems will get infiltrated by police, with a 'security update' being pushed that surreptitiously breaks the encryption?
Banning e2e encryption would do pretty good at moving almost everyone of off e2e encryption I think.