I think that to find out the requirement for a power assurance check you need to start at the top:
Does your aviation authority, require you to operate PC1? If so then you must comply with the RFM requirement for CAT A operations including the limitation that "CAT A Ops are prohibited if your engines don't pass a power assurance" and the instruction in each individual take off profile to " Carry out daily power checks in accordance with ENGINE POWER CHECKS procedure in Part K Common Performance"
I think the inference is pretty clear that you should conduct your daily power assurance prior to operating CAT A that same day.
Having said that, I can see Outwest's point of view. Which power assurance is more valid out of these two:
1. You have the first flight in the morning and a power assurance was conducted after last flight the day before. Technically you can't use that power assurance for a CAT A take off even though the aircraft has not flown since and has probably also had a compressor wash.
2. You have the last flight of the day and a power assurance was conducted that morning. Since then the aircraft has flown 10 hours in a salt laden environment without a compressor wash. Technically you are good to go for a CAT A take off.