Amazon's goal should be for it's apps and services to be fully competitive with everyone else's regardless of what phone they are on - iPhone, Nexus, Galaxy, Fire, shouldn't matter. I really don't see what the problem is with having Amazon's apps and services installed on the phone by default right alongside the ones from Google. Let the user decide. If users tend to prefer the Google stuff to Amazon's then they're not going to buy an Amazon locked-in Fire phone anyway.
Amazon's problem is that their apps don't come pre-installed on anyone else's phone by default. Making their own Fire phone solves that problem. It doesn't solve the problem of making Amazon's apps actualy competitive with everyone else's. That problem can only be solved by actualy making their apps good and desirable. If they aren't, locking Fire phone users into them isn't going to help sell any Fire phones and therefore isn't going to help gain exposure for Amazon's apps anyway.