Reddit pointed me to https://community.infiniteflight.com/t/why-are-airline-names-plural-e-g-why-is-american-airlines-not-called-american-airline/174997/16, which provides the following answer:
Well “airline” has become a normal term for us to use now. When airlines were founded, using “airlines” and “airways” would have been more related to the routes the carrier flies. Hence some airlines were called “Air Lines”.
https://books.google.com/ngrams/graph?content=airline%2Cair+line%2Cairlines%2Cair+lines&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3 indicates that the term airline was rather new when these companies were created, and the term "air line" is older:
