Do you think that as you advance in rank and skill set should you remain proficient in the lower skill sets

Each of the "lower" skill sets are building blocks for the "higher" skill sets. I've done the intelligence and you honestly can not be good at what is expected of you at higher levels if you can not master the starter set.
Skill level 1
Skill level 2
Skill level 3
Skill level 4
Collective skills
If I remember right, one of the tasks at each level is to be able to evaluate the effectiveness of juniors at each skill level. If you can't do a skill level 1 task because it is "beneath" you, you can't perform your skill level task of being able to evaluate the performance of a Soldier.

Part of me has a problem with this question because it stinks of "privilege". Not all situations, like not all Soldiers, are equal. There are times and assignments where you may not have a team of underlings available to perform all the tasks that you have "gotten away from". There are Soldiers, that regardless of the fact they got through AIT, will never learn to be good at their job. And Chelsea Manning's supervisor... Do I need to say more?

How do you expect to train your troops if you don't stay proficient in all aspects of your job.
When I was a Platoon Sergeant in a Corps Radio Battalion, I had 26 31Cs & 31Ms. My MOSs at the time were 31C & 26Q. I had to go to school for Multichannel Communications just so I could keep up with my platoon.

Another old saying, "never forget where you come from".