There are a number of institutes/colleges dedicated to language learning in the US: Alliance Française [0], Goethe institute [1] with multiple satellite offices around the country, all offering language classes for a few hundred dollars.
There are a multitude, nay - infinite! number of online classes with teachers who will use "traditional", textbook-based approaches. [2]
Young Americans regularly go for 1-2-3 month trips to Italy, France, Germany, etc. American passports give folks a ton of latitude. You can stay in a hostel and eat cheaply - many thousands of people have done it.
I'm not saying it's easy, but I will definitely push back on the idea that it's impossible.
(and will also absolutely agree that the convenience of an app will be 10,000,000x more tempting to use than doing any of the above)
[0] https://www.afusa.org/
[1] https://www.goethe.de/ins/us/en/index.html
[2] https://www.italki.com/en/teachers/french