Even if we suppose that only reasonable warrants would be granted for the use of such a backdoor, the backdoor is software, and does exactly what it's programmed to do - as anyone whose written software knows, this is sometimes not the same as what it's supposed to do. This means that bad guys can readily exploit any backdoor. A human would reject such accesses as obviously unwarranted, but a computer doing exactly what it's programmed to do won't.
Similarly, in Ethereum, a contract does exactly what it's programmed to do, not what it's meant to do. When malicious actors exploit this for personal gain, our reaction is that we should to "fix" the currency to be in line with our human judgement about what it ought or ought not be used for.
In both cases, you can't have your cake and eat it.
With backdoors, you can either have a simple, automatic means of investigating suspects, or you can have human judgement as to whether or not such searches have value that exceeds the value of an individual's right to privacy.
In Ethereum, you can either have autonomous and decentralized contracts, or you can have contracts that are subject to human judgement and values.
I'm still very much in "Micheal Jackson eats popcorn" mode with respect to Ethereum, but at this point it seems like it's trying to accomplish two things that are fundamentally incompatible.