Parameters of the type "date" should have some way of autofilling with today's date. They shouldn't autofill automatically without any user input, because this will cause unexpected edits. But autofilling should be made as simple as possible.
The difficulty is that different wikis and even different parameters in different templates may have different conventions as to the preferred date format. However, it's also possible that there is already a cross-wiki convention (I just don't know), given that the TemplateData documentation suggests yyyy-mm-dd
Using the default date manager of the browsers (<input type="date">) doesn't work because it inserts dates in its own format (dd/mm/yyyy). It also breaks the current layout.
The temporary solution is showing the current date as a placeholder with the format recommended by TemplateData, yyyy-mm-dd. This has the advantage of not forcing any format, so each wiki may use their preferred format.
Maybe the best solution is having a button to the right of the date fields that autofills the date, and set the preferred date format from a configuration option, so that it can vary per wiki (but not per template or per parameter).