The paralyzed condition notes
A paralyzed creature is incapacitated (see the condition) and can't move or speak.
Under incapacitated it says
An incapacitated creature can't take actions or reactions.
I mistakenly thought that my character could issue mental commands (to control a spiritual weapon perhaps) while under the influence of a hold person spell. However, as has been noted on the site already, paralyzed creatures are incapacitated, and therefore can't take actions, and therefore can't take bonus actions.
I'm wondering what issues could arise from allowing paralyzed creatures to take actions that do not require physical movement. I'm particularly concerned with in-game logic, game balance, and ease of play, but there may be other issues that pop up that I haven't considered. It might also be possible that such a change wouldn't cause any problems.