Having used Java somewhat, the biggest pain points I encountered with checked exceptions was their incompatibility with highly generic code (aka streams). What

Having used Java somewhat, the biggest pain points I encountered with checked exceptions was their incompatibility with highly generic code (aka streams). What if all library functions taking lambdas (e.g. map, filter) all took throwing functions as parameters (i.e. have an extra generic X argument for the exception type, like R apply(T arg) throws X) and simply rethrew those exceptions, AND have the exceptionless functions (R apply(T arg)) be a subtype of the throwing version so they are compatible? I haven't touched java in a while so I may have forgotten a thing or 2 about its type system