Would it be possible to set the course to automatically change keyboard layout?
Depending on the answer, I mean.
Yes, Google translate does have the function, and it would probably be even easier for Duo to implement, as Duo know what language should be input, whereas Google translate does not, always.
I don't see why . . .
But, of course, you have no idea what resources are available to Duo at this point, nor do you know what they are working on. Who says it's impossible? They just have chosen not to do it yet.
I'd much rather see a new language in the incubator than have Duo implement a function that we do just fine without.
You are right, Duo is now only producing user-developed courses. But Duo's staff has to support course development. They need (it seems) logistical and (maybe) some programming support for each new course. This limits the number of courses in development at one time to fewer than those that competent developers have already applied to create.
Duo has said in the past that they lack the "bandwidth" to develop lots of new courses at one time. My contention is that this "bandwidth" would be lessened if Duo assigned a programmer or two to work on what you suggest. But I may be wrong. Duolingo never really explains what it's doing or how it does it. We can only guess what Duo really needs to support a course.
Probably the infrastructure is lacking.
The server would need to send some language/input specifications via http to the browser, and the browser would then need to ask the local operating system to change the input method.
I do not see any reason that this could not be feasible, but
I doubt the infrastructure is in place
There may be security concerns about allowing server-based request to change the user's input method; this could be maliciously annoying