Its not about any of those states IMO. I open I channel, I specify the size of that channel is SATs not USD, so capacity should be measured in SATs. It surely is the natural measurement unit for this application.
Discussion
Just because roads are built in tons of asphalt doesn't mean that tons are the relevant unit for the road's usage or its collective ability to move traffic.
Similarly, lightning channels are created in sats but the relevant metric for its settlement capability and economic utility is the same metric used for the pricing of goods, which is USD for direct comparison to other economic systems.