If you're an expert pianist, you ought to be able to reproduce a simple tune on the piano, by ear and blindfolded. If you're an expert skier, you can ski backward and ski on one ski. If you're an expert chess player, you should be able to memorize any chess board at a glance. If you're an expert mathematician, you should be able to do simple integrals without reference tables. Those are not skills that you need, they are skills experts simply can't avoid acquiring as part of working in a field for many years.
Likewise, if you're an expert programmer, you should be able to write bubble sort on the whiteboard without a web search. If you're an expert Python programmer, you should have worked enough with strings so that you don't need to look up trivial functions anymore. Those skills are indicators of your experience, not specific job requirements.
Plain and utter nonsense. All the skills you mentioned above are acquired by repeatedly doing a move or a task over and over again. Programming is doing the exact opposite and having the machine do the repeating - if you are a good programmer. Memorizing bubble sort is beyond pointless for a seasoned programmer. To the contrary, if you can still recall bubble-sort, you're probably not that seasoned yet.
If you test problem solving in a job interview for programmers, you're good. If you're testing for by-heart reference knowledge, you're being silly. Perhaps the nearest equivalent would be to test how fast a programmer navigates his favorite development environment. That might actually be a useful test, vis-a-vis asking for him/her to recall bubble-sort in PL X,Y or Z.
You got it totally wrong and missed the core and prime difference of programming to performing arts, sports and whatnot.