1. Eager, not lazy - I think it was a mistake for the promise constructor to take a function, and in that way lead the users to believe the promise represents a computation. Creating a pair of promise and future (the latter as the producer side, like in C++) would be much cleaner. I disagree that lazy would be more general, you can simulate lazyness with functions, but you couldn't eliminate the performance cost of creating the unnecessary closure with a lazy solution. Regarding getUserAge - the common case for that function would be to take the user ID as the parameter (and hence would be lazy by construction), the parameterless version is a special case.
2. No cancellation - cancellation is much better represented with cancellation tokens (even C# Tasks cancel with cancellation tokens, so does fun-task mentioned at the end, though in non-composable way) - you cannot build a generic solution that can cancel the right computations. With cancellation tokens it's clear what cancels what.
3. and 4. (as well as being allowed pass non-promises to places where only promises make sense, like Promise.all and await) are unfortunate accidents that make typed environments (e.g. TypeScript) harder to work with but are not that important as 1 and 2.