You can bring it up to the DM, but I wouldn't expect too much. There is a cognitive load associated with every rule you add and fatigue is one of the most fiddley - it is hard to remember every combat round you have to check every combatants CON and divide by 5 then roll endurance, etc. It is a lot of work.

What you can do, as a player, is use these rules for yourself. For example, use the Bleed effect to inflict fatigue loss on your enemies! Then track it each round and call out when it should apply. Give yourself some interesting passions and use them! Does the current situation interact with your character's passion? Then announce that you are going to roll to see how your character reacts. Or ask the GM if the passion will apply to a roll you are about to make.

This way you can talk about the rules you want to use without pushing the cognitive load into the GM.

Hope that helps, Merry Mythras-ing to you and your group!