BartK Maybe I should try to clarify what I meant by not always prioritising steady tempo when reading. We all have different backgrounds and struggle with different things. My point was to keep the practice material at a level where you are slightly challenged and out of your comfort zone regarding your weakest skill. Something else will probably have to give a little if you are really trying to be at that optimum challenge point that requires almost all your focus. If it is difficult to clap the rhythm along with a slowly ticking metronome disregarding pitch, that should definitely be practiced. If it is difficult to read pitches or chords disregarding rhythm, that should likewise be practiced in my mind. Same with articulation and dynamics. The material where you can do it all will naturally have to be easier than the practice material that more effectively grows your abilities.
If you are playing with others or in an examination / performance situation the priorities are of course different. Thus practicing sight-reading for those situations would also be different than practicing to read piano music at all. Like you, in that case I would absolutely prioritise timing, dynamics and articulation way over getting every single note in and, when applicable, with good intonation. But knowing how to simplify is an art in itself and requires being able to read the "big picture". A beginner will first have to learn to read at all.
Many adult beginners have played other instruments or sang in choirs before starting piano and are already relatively experienced music readers. For me personally, after decades of playing the clarinet, my rhythm reading is many levels more solid than say my instant chord recognition. Looking at your example, I don't need to analyse the rhythms, like "Oh that's an eighth note on the downbeat followed by a triplet during the next eighth." As children where I grew up we were taught to read rhythms using some variant of the takedimi approach and I still often think in similar terms. That means that for me the rhythm of the first beat would already be chunked into a "daa-di-di-di" unit in my brain and it would take a minimum amount of effort to read it and leave plenty of head space to add the pitches of the monophonic melodies in the (also already chunked) keys of a minor or d major.
Mathematically there is only a limited number of ways you could subdivide a beat into tones and rests, assuming the classical musical standard of dividing primarily at the halves, quarters, eighths, thirds or sixths and sometimes fifths, sevenths, ninths or twelves. Other subdivisions will be much more rare. With enough practice or exposure, all the common ones (including everything in your example) will be chunked in your memory and read effortlessly. At least that is my experience. But add some harmony or polyphony to your example and I would struggle a lot to keep in time without skipping anything because of the sheer number of notes and that I don't yet have all chords chunked in my mind to nearly the same level as I do rhythms, and might have to actually read individual pitches. And I don't yet hear most chords in my inner ear the way I do melodies and rhythms just by looking at the sheet music. If reading the simultaneous pitches is my biggest struggle, that is where I'll focus my attention for now. And that is the reason I'd slow down the tempo if it gets tricky, even when I have no problem clapping the rhythm on its own.
If I were reading as a first step of actually learning the piece, not to practice reading per se on "discardable" material, I would normally divide the piece into such short segments that I could make sure to be able to practice them each correctly in rhythm - if necessary at a very slow tempo to begin with. Not saying that I would then always practice in correct rhythm. There could be times when I would deliberately alter the rhythm in order to work e g on speed bursts with the goal of eventually being able to perform at a faster tempo.
