You didn't specify that you were only speaking of your own lessons
Sorry, I really thought using the word "I" was enough to specify this. Yet I doubt that I am so special that nobody else would share some of my experiences...
You don't forget an f sharp unless your head isn't in the right place during practise.
Exactly. But what you don't seem to accept is that it is not always a conscious choice to be focused or not. Most of us amateurs do not have the luxury to choose when we have a piano lesson, mostly not even when we practice. We may be really tired from work and have other reasons why we suffer from distractibility and disorientation. Some of us may even suffer from ADD/ADHD or other types of attention deficit problems. There are also so many ways the situational factors affect one's concentration. So you have no way of knowing whether the OP can just by will become focused enough to benefit from regular reading exercises on lessons. That is for him and his teacher to find out. You offer a solution to the problem (focus and let the teacher do his work), but without taking into account that the solution is adequate only if certain basic conditions are met.
Have you worked with an adult who have attention deficit disorder? I have (computer programs, not piano). If you just tell them to concentrate and push them to keep going it often only gets worse, their mind goes blank. They may need a lot of quiet time to be able to refocus back to the task, and they are often well aware and very frustrated/anxious of their inability to do so while someone is waiting, which is working against them. This probably happens to most of us every now and then when the conditions are against us. To get over this it's usually better to redirect the focus to something less taxing. This is what I meant when I talked about wasting lesson time, to keep going with an exercise when clearly the student is not ABLE to focus enough. It is much better to move to something that does not require as much multitasking and focus and by doing so get over the anxiety which is blocking the mind. IMO a good teacher will either adapt to the student with such problems or accept his own limitations and refrain from teaching them. Not everybody can handle special education either; it requires a lot of specific knowledge and patience and probably also some life experience.
I used myself as an example, didn't say what you propose never solves problems. With an average kid it often does because they simply haven't learned to focus and control themselves yet. It's less likely to be the only problem with an adult. To be able to read notation, and especially something I haven't looked at before, I need to be able to focus 100%. If not, both my visual abilities and my memory recall suffer badly. Also I must not be tired and I also need a very clear print, good light and don't do well on a grand where the sheets are higher than with an upright (because of my tension neck problem). Not all of these conditions are met on my lesson.
What I have learned at home is that I can usually work myself into a better focusable state by just sitting on the piano doing tasks which require less multitasking for a while (half an hour or so). This is little help when a lesson lasts 45 minutes. The other option would be to have a warming up session before the lesson, but it is not possible either. Also if I only practiced while well focused already, I would probably be able to practice 1-2 times a week which simply is not enough. I adapt my practice and we adapt my lessons instead of banging our heads to the wall trying to adapt me and my other life which is not possible.
I’ve been with my teacher 2.5 years now. We do try sight reading every now and then, and I try to stick with it even on a bad day. Most often I end up with a headache (literally) and the rest of the lesson suffers as well. There's little to gain from repeating the experiment on every lesson, since we both already know quite well where my issues are. I work on those on a better time, which just happens to be at home. If I could invite my teacher over those times, I am certain we could have some beneficial sight reading sessions. But the world is not perfect.