I under promise for my sanity.
If you’re using the shipping automation, you are not either ‘over’, or ‘under’ - promising. Amazon is setting the promise for you.
Mainly UPS.
If you ship by UPS, the automation should do an ok job. But a manual template set-up would do an equally ok job. It’s Amazon’s bogus claim that the automation is “better” that’s all f’ed up.
But with UPS shipments, it’s 6 of one (automation), half dozen of the other (manual set up). UPS transit times from Point A to Point B are highly predictable and don’t vary much. You gain nothing with the automation, but don’t lose much either - unless you’re expecting it to do all the stuff Amazon promises like increase your sales.
So far, knock on the wooden stove top cover, UPS has been reliable for me.
Carrier reliability isn’t really the issue when it comes to the automation. It’s simply the ability to predict what the carriers will do. For UPS and FedEx, it’s pretty simple (which is why the automation can handle it) - Point A to Point B takes X days.
USPS is far more variable, which is why the automation can’t get this even close to right. The automation has always been unable to figure out what is needed to allow you to buy the label you want through Buy Shipping too, although that may be improving, as I’ve noticed changes within Buy Shipping lately.
But anyone who trusts Amazon’s claim that they use carrier data to make highly accurate predictions about transit times is foolish, at least when it comes to USPS services. They haven’t got a clue.
If my stuff were small and shipped USPS I’d be concerned about “peak” times.
It isn’t peak times that are the issue, it’s that the automation has zero knowledge about actual USPS transit times, and Amazon’s claims to the contrary are flat-out lies.
My first-class packages go from OR to FL in 2 days about 2/3 of the time, and 3 days the rest of the time. Why? I don’t know. It’s not supposed to be that fast, but I can look back at years of deliveries and tell you that’s how long it takes. Amazon’s automation says it takes 5 days. Nope. Not hardly ever. Maybe once in a blue moon.
Buy Shipping is also convinced that OR to FL takes 5 days, so I set that as my manual promise to ensure I can buy a FC label through Buy Shipping. If not for this, I’d give FL buyers a 3-day transit time because that’s how long it actually takes.
If Amazon’s automation could do what it claims, that’s the time it would set. But it can’t, so it doesn’t. They’re just clueless when it comes to USPS. 
They’re better with UPS/FedEx but again, they’re only doing the same as you could do yourself with a manual set-up. They aren’t giving you anything better as they falsely claim.