One level of getParent() is useful to avoid having {{#invoke:}} used directly while keeping the wrapper template simple by not having it have to manually pass through every parameter. Additional levels seem more likely to be confusing and fragile as the template containing the invoke starts to depends on the context where it is called.

In T196501#4258900, @putnik wrote:

For example, you want to prevent the use of the Infobox template directly in articles. But the module can not get this information.

That doesn't seem like something that is all that useful to enforce via a module, rather than by community convention in the same way we typically avoid putting {{#if:}} directly in articles.

A typical cascade of template calls before the module is called is 3-4, and these templates can contain parameters that the module needs to know, or which it is desirable to proxy into the module.

And if the module starts to depend on those 3-4 levels of parents for parameters, it makes the whole stack dependent on those 3-4 levels existing and maintaining the same parameter names.