And even if you want a prime badge, it's often/usually cheaper to go with a 3PL that can do some sort of SFP setup if you have reasonable volumes.
Although Amazon has a stranglehold on 3PL's too (or if you are a seller offering SFP), as they will force you to use Amazon Logistics at a certain % of volume if you want the prime badge which can be more expensive than other carriers.
(I work in logistics consulting and do network strategy design & 3PL selection as part of that so have a reasonably up to date view on comparative/competitive costs for this sort of thing - mostly in Europe though and appreciate the USA market is different)