- That the government has not demonstrated that delving into the user's private search history is relevant or may advance the case at all,
A search warrant merely needs probable cause. One user's history seems like "a particular place or thing to be searched". The gov't doesn't have to prove that any evidence seized will even be used.
- That the data is not the property of the individual but rather a trade secret, or
That might work for a civil lawsuit, but it's absolutely not gonna fly in a murder case.
- That Amazon is an unrelated 3rd party and should not be compelled to cooperate in something which it is peripherally related.
Doesn't work for banks, telephone companies, Internet providers, etc. It doesn't work for a retailer with security cameras. This also isn't a fishing expedition; it's probable (at least according to the judge who approved the warrant) that Amazon has evidence that may be relevant. Besides, for all we know, they have exculpatory evidence. Both sides have the right to compulsory process.
All that said, I have a modest proposal.
If Amazon intends to keep recordings and use them for profit, they should be compelled to produce those recordings when the public interest so demands.
If Amazon wants to be exempt from that, they can submit to rigorous and frequent government audits to prove they are not recording anything, in the public interest of privacy of citizens.