I routinely use different passports for different flights on the same booking (a US passport and an EU passport) because I am typically flying between the US and the EU. Once ETIAS goes into operation, this will likely become even more common, as there will be additional motivation for dual US/EU citizens not to use their US passports to fly to the EU.
Why will ETIAS add some motivation for dual US/EU citizens not to use their US passports to fly to the EU?
ETIAS stands for European Travel Information and Authorization System. It is a completely electronic system which allows and keeps track of visitors from countries who do not need a visa to enter the Schengen Zone. From the end of 2022, all US citizens traveling to Europe for short-term stays will be obliged to have an ETIAS visa waiver with them before their trip.