Would it make sense to have an option under direction cosines to adopt the orientation of a specified element?

It would reduce redundant input, particularly on arbitrary-angle head nozzles.

You currently have the option of adopting the direction cosines of the previous element. Is this what you mean, or do you want the ability to select any arbitrary element?

Perhaps it's a matter of working against anticipated modeling order.

Node 10-20... first pipe flange. Anchor on node 10, cnode anchor to 1010. Vertical orientation.

Node 1010-1020... nozzle flange.
Node 1020-1030... nozzle neck. Nozzle flex node 1030, vessel node 1040.
Node 1040-1050... vertical rigid component from vessel head @ nozzle to weld point between head and vessel - which is an arbitrary polar coordinate of theta and r.
Node 1050-1060... rigid element from node 1050 to CL of vessel at head.

It sounds like the order you have in mind is:
1. vessel shell
2. head component, looks like vessel shell
3. rigid element to polar coordinate
4. nozzle neck, and it adopts the previous element's coordinate as the vessel axis.

The current method makes sense, but is somewhat obscure if you don't normally model in that direction, but might not be encountered frequently.

Is that orientation corrected if the nozzle rotates relative to the vessel after the fact? I'll have to test it next change I get.

the vector cosines should be the cosines of Node 1050-1060... rigid element from node 1050 to CL of vessel at head.

Agreed - the request is to tie it an element not due to not knowing what to input, but to avoid repeat entries.

I can see an instance of orienting the nozzle in the wrong direction, copying the cosines, and then later adjusting the orientation in the piping arrangement, but forgetting to adjust it as a duplicate entry.

Ok, there is an alternative. Model orthogonal the equipment and nozzle limit check and then rotate all elements. this way you will not repeat the vectors input. It will rotate the reference vector as well.
I guess anything may be improved in the software but with what effort?