You only consent to allow delivery people into your home, not the police. The 4th amendment doesn't have a trickery loophole, your reasonable expectation of privacy is always with respect to the police, not to other businesses and people you give trust to. The police can't set up a fake carwash and then warrantlessly search all of the cars that show up just because you're handing over the keys and consenting to let strangers in. Your home would be no different.
Another, perhaps better example: a landlord typically has a set of keys and the right to access a tenant's apartment. In a commercial building, those keys could be held by any number of "strangers" on the maintenance staff. The police still need a warrant, they can't just ask the landlord for a set of keys. That's really not any different from having the "keys" held by Amazon staff members.
There are lots of instances where a person's expectation of privacy is low with respect to specific people/businesses but high with respect to the government, and that doesn't weaken their 4th amendment protections.