I don't think we need another denomination for units. Even dollars don't have three denominations, it's just dollars and cents. I also agree with @Car who said on SNL that "bits" demeans the value because it's associated as ephemeral 0s and 1s.

I wouldn't mind changing sats to Bitcoin. At some point, 1 Bitcoin will be such a large denomination of value that it won't be useful as a unit of measurement.