" A function for Insert Current Date would do that, I think. Is there such a thing?"
The function is "TODAY", and like all functions in Numbers, it is active at all times, meaning if there is a change to the table,* the function recalculates and the cell containing the formula containing that function displays the newly calculated value.
Functions continue to act in that manner today, but can be sidestepped using the copy, thenPaste formula result actions described above.
The calculation can also be done in an Applescript, or using a Service (which may be based on a Applescript) which will insert the date or the date and time into a selected cell as a stable value not attached with any function or formula.**
Applescript (and Service) solutions are not automatic, though, as they require selecting a destination for the output and user action to activate the Service/Script in order to have it calculate and place the result.
SGIII developed several Services several years ago, and offered them as a download to those asking in these discussions for assistance with the tasks they could be applied to. That those offers have not been posted recently suggests to me that the services no longer provide a great improvement over using what is available (in this case, using formulas, then Copy > Paste formula results or using Table (menu) > Insert Date or Table (menu) > Insert Time.
Regards,
Barry