I believe everyone should skate compromised (tired, sore, hurting, etc.). Hopefully most of us have a lifetime to skate, so I am happy to miss a few days because I know I will be back BUT I also know it helps to skate a little every day.
On a compromised day it’s not about productivity for me, it’s just about skating and doing what I can comfortably. My front leg quadriceps have an issue right now but I got a mini session in yesterday, 15 minutes of getting a line together of all my simple moves (I can only do about a half-dozen things on a skateboard right now). Still, spending a few minutes just accomplishing a simple line feels like a big deal for my emotional and mental state.
If you make it about “being productive” it can be tough. I try to get something steezy in when I am compromised and make it about being “future productive”.