wrote:

I believe the rule is that if there is a departure procedure
published, fly the departure procedure.

If there is an approach chart published, but but no departure
procedure, the rule is no turns before 400' AGL, and maintain 200 FPNM
and you will be clear of obstructions.

Known as a diverse departure area as per the AIM

No approach plate, you are on your own.

Does this not cover everything?

No. The runway has to have published IFR takeoff minimums AND no ODP
for you to make a diverse departure.