I have noticed that when I give companions the Shishkebab, they don't seem to swing aggressively with it -- they seem to wait several seconds between hits. This makes me wonder if there is a problem with the NPC combat AI, where if they are using a weapon that has a damage-over-time aspect, they will wait for the DOT to expire before attacking again. Obviously this greatly reduces the damage they do with such weapons and probably makes them poor choices even though they look impressive on paper.

Has anyone else noticed this?

It might depend on which follower you give it to. Clover is especially awesome with the weapon. She runs in and starts hacking in my experience. I tried giving it to Jericho once, but he constantly eschewed his Heavy Incinerator for the Shiskebab, and I had to take it away, because he kept rushing in and dying.

Well, if you have a damage over time weapon, you want to allow the damage to take place at least somewhat prior to attacking again. Otherwise, there's no value to the DOT element and your total damage is lower than the weapon's potential.

I use Shojo Companions with TRASCH and Sharing and Caring Companions, and I alter their combat strategy for different contexts and weapons.