I'm an SE at Nutanix, and I've seen both cases from this thread several times:
1) Customers want to go to AHV and are looking for a great backup solution at the same time, and currently the strongest contender is Commvault
2) Customers already have VMware + Veeam, and will move to AHV, but would like to keep the Veeam solution if possible.
License savings is one reason they want to go to AHV, but it is not the only one. Another reason is the ease of use associated with AHV. The Nutanix platform + AHV combination honestly is much simpler to use than other hypervisors. If you haven't seen it, I can show it to you over a 15 min webex (or visit our booth at a tradeshow where we both are present, for example). Switching ESX for Hyper-V does not include this benefit. Some might even argue it's a step in the wrong direction.
Another reason is support -- if you go to AHV, your whole stack (storage, servers, hypervisor) are made by the same vendor and supported by them. Sure, we support customers running other hypervisors as well, but we can't, for example, fix software bugs in the other hypervisors.
Some customers also want to specifically avoid going to Hyper-V for various reasons. And yes, the hypervisor cost is a real reason as well for many.
If you don't mind my asking, why would Veeam NOT want to support AHV? I understand you need to "sell what's on the truck", ie offer the solutions that work right now, I would do the same. But if you look at this thread, it might also make sense to add AHV to the near term roadmap? I believe it would benefit both companies, and it's difficult to see a downside for anyone? The business is there to pay for the software development required.