`unsafeBuildDynamic` secretly is ~`cacheBehavior`, can we be more explicit about all ways to cache Behaviors?

[parenthetical]

From its documentation one might think that unsafeBuildDynamic simply puts an Event and Behavior together into a Dynamic without any further effects. However, in the Spider implementation it actually does a hold on some starting value sampled from the input Behavior and the updates of the input Event.

This in effect makes unsafeBuildDynamic a function that caches a Behavior's value in-between update occurrences.

There is another way Behavior values are cached, but only for the current moment (frame). This is achieved via the PullM type: sample turns Behaviors into PullM values, which can be combined in arbitrary ways without any caching, and pull turns a PullM value back into a Behavior.
Such a Behavior's value is computed only on-demand, but its computed value is retained for the current moment/frame.

Because the only way to construct Behaviors goes through PullM and pull, it's IIRC not possible to "map cheaply" over behaviors like we can do with events.

Can we create a scheme where we have functions like cacheBehaviorNow, cacheDynamic, and mapBehaviorCheap?