It would be worth applying for the passport card even if it did not fit in the wallet just because it is another proof of US citizenship. It cannot be used for travelling abroad by air, but it can be used for I-9, as a REAL ID, and as a proof of US citizenship if you lose your passport book and need to deal with the US consulate abroad.
When I tried to buy alcohol with my passport card as an ID (just for fun), the store clerk did not even know what kind of document it was, and was very surprised that it had a "strange" date format and term "surname" instead of "last name". For her it looked like a foreign document
Oh, ethnocentrism at its best...