In this answer to the question of why zero-visibility landings are legal and routine but not zero-visibility takeoffs, the poster makes the following point:
When an aircraft lands in near zero visibility, it is a fully automated process that is actually done without input from the pilot. The pilots are only needed to taxi off the runway and park the aircraft. It is called "Autoland" and many of today's aircraft have it.
As of today no manufacturer has designed an aircraft with "Auto Takeoff" but I suppose it is not impossible.
Which seems odd, given that autolanding with an ILS is a mature technique using mature technology, and autotakeoffing with an ITS (instrument takeoff system) wouldn’t need much more on top of that (just some additional antennae on the aircraft’s tail and a couple new routines for the autopilot) - it’d mostly be pretty much an ILS running in reverse, something like this:
What’s the dealbreaker for an autotakeoff-supporting instrument takeoff system?