Why do some airlines ask for the reason for travel when booking domestic flights within the US?
As far as I know this is purely a marketing question, and will usually be optional.
You can find such questions on airline websites but also hotels, railways, and more, in many countries. In most cases the question is asked during the booking process, sometimes they ask the question upfront in search parameters (in which case it may have an influence on what fare types they put forward).
Apparently the answer to that question is useful to them for reporting, to optimise their yield management, communication campaigns and whatnot.
It may have an influence on what additional services they put forward, or they may take that into account in overbooking ratios.
Another possible reason is that some agency at either end wants the info for their own statistics.
On some sites/apps this allows the user to filter past bookings (so if you use the same account for business and personal trips, you can easily find the business ones for your expense reports), or may change the payment method (e.g. Uber allows one to save one payment card for personal and another for business), but in the latter case this is usually quite a bit more explicit.