What are the key assumptions that an enterprise should make about migrating to the cloud?

Firstly, that the people you have now may not have the skills you need for tomorrow.

Secondly, that it is better to invest in the people you have before you try and hire the skills you need.

First coach, then poach.

That after all is said and done, it is not necessarily the case that the cloud is cheap, better, faster.

That cloud will be more expensive than on prem (often times) and that you will have a challenge to find enough adequately skills people to execute the migration. The skillset is fairly different, and those cloud folks are in very high demand and hence being poached all the time. You will also need to be ready for it to be significantly more risky at least initially as cloud is very prone to misconfiguration related security issues vs. your on-prem legacy systems that are more locked down.

Herbert Fuchs would love your input as well!

Here are a few:
All applications cannot (and some probably should not) migrate to the cloud. Lift and Shift may be an attractive interim solution - but consider the costs of networking, bi-directional data flow, and other cloud costs while thinking of that solution. Consider partial refactoring at least for some apps before looking at complete refactor of heritage apps.

There isn't really an easy button to move assets to the cloud, however glossy and attractive the markitecture and website are. Unless you invest in an abstraction layer (like Tanzu Application Service or VMware Cloud - not so subtle plug here). If you are thinking hybrid cloud strategy, then I would urge you to consider these - saved a ton of time for us to transform our applications.

Have a robust software factory approach with good app sequencing as you migrate your apps. Needs to be based on value and not just revenue or technical debt. More than happy to have in-depth conversations around this!

There will be a large learning curve with your devs and IT operators in learning the new software supply chain and retool your pipelines. Try to automate as much of manual toil as possible. 

Observability, governance, and management of your cloud assets are critical. You need a good plan for lean cloud governance, observability, and spend. Understand your SLAs/SLIs/SLOs and what you have committed to your customers. What happens when you have impact through your chosen IaaS? Again - hybrid cloud/multi-cloud helps with this.

As you are shifting from CapEx to OpEx, there might be ROI models that you need to adjust or revisit so that you know your spend and don't get a nice hefty bill at the end of the month.