Yeah, I would agree. I seem to come across Cb (enharmonic to B) quite often, usually in an Ab minor chord. E# and B# I’ll see most often in the context of an augmented A or E chord. (Or as a passing chromatic tone.)
Pianos are tuned to an equal-temperament scale, so the frequency ratio of notes E and F is identical to that of D and D#. In that sense E# = F.
However, equal-temperament is a compromise (so that pianos don’t have to be retuned for different keys) and is not fundamental to the nature of music. For example, the Major Third interval (C-E) is intended to be notes in the ratio 5:4 (1.25) but with equal-temperament the ratio is imperfect, 1.26. Equal-temperament is the assumption today, but it needn’t be so: Mozart and Bach (with his Well Tempered Clavier) used their own tuning methods. In a violin using just temperament, E# will indeed be a slightly different note than F.
Read some comments here or a discussion at a well-known message board.
Should we tell the OP about double-sharps and double-flats?
Only if you agree to clean up any mess generated by any poo-flinging from the nitpickers or asploding heads.
Although I have never seen one in the wild, and I am a little unsure as to the music theory reasons one would ever choose to notate it this way, even triple sharps and triple flats have been seen in music. See under "3. Extreme accidentals.
Double sharps and double flats, though, are common enough. (See, for example, the C diminished 7, with a double flatted B, enharmonic to A. For double sharp, see something like B+/B augmented.)