510.2.-510.5. Ruling on priority

[Wingnut]

However if no ability hit the stack why would either player gain priority as there is nothing to respond to as you are unable to respond to damage assignment and dealing of said damage according to the 510.2.-510.5, rules?

Every time the game goes from one phase into the next, priority is passed. Every time. Going from first strike damage to normal damage is considered changing phases. So you cannot respond to the damage itself, but both players have the ability to cast instant speed spells at the end of first strike damage phase.

[Ekann1]

If there is a chance where people COULD get priority (maybe made because an ability might have to trigger), they will get priority even if there are no abilities that do trigger. I don't really know why besides what remillo said, that's just how the game works.

[Remillo]

If there is a chance where people COULD get priority (maybe made because an ability might have to trigger), they will get priority even if there are no abilities that do trigger. I don't really know why besides what remillo said, that's just how the game works.

The easiest was to see this is in the Untap step with Inspired.  While the trigger goes off during the Untap step! it doesn't get put on the stack until the upkeep, which is the next time a player could get priority.  It's just how the game works,and it makes sense.