If they're so busy NOW because of panic buying, why are they waiting until JUNE to suspend the service? You can't be that big of a sucker to believe the PR. The Amazon shopping surge is simply the easiest excuse for the average person to believe.
This is what they told their customers:
At Amazon, we regularly evaluate the requirements of our businesses to ensure we are structured in the best way possible to meet the evolving needs of our customers. After careful consideration, we have decided to pause our Amazon Shipping service in the US. Our last day for pick-ups will be June 5th.
That sounds a lot more like "Our attempt to compete with FedEx and UPS isn't really geared to meet the evolving needs of our customers" than "This thing is working out so well that we have to let it rest to fully appreciate how well it's working."