Update number 2: I asked this same question on an air travel related board a few days ago. Most people concurred with my conclusion that it can’t be done anymore, but then one person demonstrated that, at least in theory, it is still possible.
To summarize what they said, a ticket can consist of multiple fares from multiple airlines, but they have to satisfy “combinability rules”. The reason I can’t book that specific routing is because there are no UA SMF-ORD fares that are combinable with any AA ORD-LSE fares. But there are workarounds one can use to trick travel sites into issuing that ticket. They demonstrated that if you use the multi-city tool and pretend you want to fly to Mexico City, with a multi-day stopover in Chicago, and make a side trip to La Crosse during that stopover, it will issue a single ticket for that whole itinerary. Presumably this works because the airlines do allow the SMF-MEX fare to be combined with the ORD-LSE fare.
Of course that would mean buying a ticket to Mexico City that I don’t intend to use, and would more than double the cost of the trip, so it’s not worth doing. But it does demonstrate that it’s at least theoretically still possible to combine UA and AA flights on one ticket, in some cases.