That's an interesting thing to consider.

Unless they subsidize, New Glenn will have to be quite expensive. As the announcement says, they spent 3.5 billion just on a factory and a launchpad, and they are years away from launching.

Amazon, as such a high visibility public company, may have a hard time justifying a 2X+ price difference versus launching on Falcons, and for Starship the difference could be significantly more.

It's also questionable if Amazon is willing to wait 3 years to get any significant amount of sats into orbit. That will give Starlink a big advantage.

Of course SpaceX also has an incentive to delay Kuiper, so they might not bid for it at all, or only provide very limited availability.