I don't know about this. I don't have prime and rarely use amazon. I ordered something recently that qualified for free shipping. I honestly felt like Amazon intentionally held my package for 3-4 days before shipping it. I think i got it in 5 business days.
I will say, not having Prime has probably saved me hundreds of dollars as I only use it for things I really need. My above anecdote was of course just that, an anecdote. Prime is core to their business though, so don't expect quick shipping.
They gave up trying to provide 2-day shipping to our rural address over two years earlier during the pandemic, and they never restored that supposedly core feature of Prime. Given that behavior, I now see them for what they are: typical rent-seeking crooks.