Just for clarity.. It is the post offices in the countries that are suspending shipments to the U.S. It isn't a ban on all shipping because companies and people can still ship by private carrier like UPS, etc. Unfortunately, there are knock on effects for private carriers and for consumers. Those companies will have to handle all of the things the postal services would normally do like the full customs process. This likely means longer shipping times and higher costs for the consumer. Private companies could also decide to suspend as well.
This doesn't make the situation any better for consumers and it seems unwise for people in the U.S. to make international purchases. Especially for bigger ticket items.