I think part of the popularity of the word “evangelical” is simply that the protestant term suggests that you define yourself by what you are not and that simply doesn’t apply to most non-catholic Christians. To define your Christian walk by someone else’s is pretty thin stuff and most people don’t, its not how most people see themselves or their Christian walk. Hence, as I say, the increased preference for the “evangelical” term rather than “protestant”.
I dare say your definition of the meaning and usage of the word Protestant is only an issue with Catholics.
Protestants, such as myself, don’t give it a second thought.
All we care about is if our hearts are right with God, has he saved us, are we born-again in spirit by the Merits of the Sacrifice of our Lord and Savior Jesus Christ?
Has he changed our hearts, making all things new and old things have passed away?
Has he given us power over the sinfullness of our lives?
The answer to a true Protestant, is yes to all the questions above.
This is all that matters, are we right with God, and a true Protestant is.