Why learn how to write if you can type?
Why bother learning how to solve a math problem if you can have a calculator solve it?
Writing on the piano is like using a pencil and piece of paper. It's slow and outdated. It's becoming obsolete when you think about it. There are kids being born that would never have to actually touch
or play with an acoustic instrument that could write whole songs, produce full albums, and even conduct symphonies without ever even having to know what a piano actually looks like. Midi keyboards
are a luxury, but you could essentially do everything you'd ever want, without ever using an actual physical musical instrument. Technology and its trade offs.
there is so much wrong with what you present as self-evident truths
a conductor may not seem to play but in most cases they have served/spent a lot of time as a performer prior to taking up the challenges of conducting
learning to write is a necessity as you cannot sign contracts with your typewriter/computer keyboard - unless you want to revert to the "his/her mark" type of signing that we saw in days past. In fact I was surprised you did not go the next step and say why bother using a keyboard when you can use speech recognition software to translate your spoken words to written words? - this of course fails because even the best software makes errors and when it doesn't misinterpret the spoken word, it may not have chosen the correct homophone (same sound different spelling - e.g. "which witch is which?" or "I don't know whether the wether will survive this weather!" (a wether is a a neutered ram or goat). In my experience most errors come from the way in which different accents and local dialects are structured - long term training eliminates most errors but they will occasionally arise simply due to variation in the speakers voice due to stress or illness.
a calculator cannot solve a problem if you do not understand the order of operations. It most certainly cannot give a "correct" answer unless the operator knows that the functions (sin, cos, tan, etc) have returned the expected answers. The derived functions (sinh, cosh, tanh, sec, cosec, cot, etc) don't enter themselves and unless you know how the derived function relates to the originating function (sin, cos, tan) the calculator will not be able to return the result expected. Doing integral or differential calculus cannot be done with most hand-held calculators and, in any case, unless the format is known in advance, entering it is not a simple process. Higher order mathematics is obviously an order of difficulty harder as well.
as for writing using the piano/keyboard you are forgetting that the keyboard is the interface not the medium. It is akin to the type-keyboard used in computer interfaces. Learning to use the interface efficiently is important to inputting your ideas effectively
I could go on for days on this but these are main concerns about your self-evident truths