Would this result in surprises like if a function is turned to async by adding an await keyword, all of a sudden all functions that have it in their call stack become async

It would work the same as it works now for generators. A function that calls a generator function isn't a generator just because of that; it only is if it also has the yield keyword in it (or yield from, which is a way of chaining generators).

Similarly, a function that calls an async function wouldn't itself be async unless it also had the await keyword. But of course the usual way of calling an async function would be to await it. And calling it without awaiting it wouldn't return a value, just as with a generator; calling a generator function without yielding from it returns a generator object, and calling an async function without awaiting it would return a future object. You could then await the future later, or pass it to some other function that awaited it.