Key signatures and reading sheet music aside, does the key a piece is written in affect the ease with which it can be played on piano?
For example, are any keys known for more difficult or awkward fingering? Is there any concept among pianists of keys that are generally considered to be “easy” or “hard”? Do piano exams tend to have certain keys for memorized pieces for beginner levels and leave others only for the advanced level?
Certainly! Fingering is one of the most important factors involved in playing piano, so where the black/white keys get pressed is paramount. Particularly in the faster passages.
One might assume that key C, with all its white keys, is the easiest, but that's not always so. Often, keys with black keys will make moving along the keyboard easier, giving room for a thumb to pass more simply underneath.
EDIT: You ask about exams, and the reflection they have on certain keys. I'm somewhat dismayed to say keys are not chosen with much relationship at all, it would appear. With all the exams I put students through on guitar, the scales and arpeggios learnt for particular grades had a large connection with other parts of the exam. Actually it was that fact that really brought it home to me (even as a teacher) how useful scales could be!
But, a lot of the pieces specified for ABRSM (don't know about other boards) bear no relationship to particular keys, thus scales and arpeggios, which seems a pity - and did nothing to clarify why I (as a student) needed to learn a particular scale from a particular key.
But there are many other aspects of piano playing that are in consideration as far as exams go, and I'm sure fingering for certain pieces in the choices is one - of many, as I say.
There are players who prefer certain keys, for personal reasons. I used to play with one who really liked F♯, due to all the black keys. It's said that a certain composer would write just about everything in E♭. Reasons unknown.
There are no hard keys - or at least there aren't once you're past the elementary stage of playing. But there are certainly phrases that 'fall under the fingers' more easily in one key than another, due to the disposition of black and white notes. As an extreme example, consider a major scale glissando. Trivial if the scale is C major. Just about impossible if it's D♭ major!
Extending the topic a little, C major is often considered the easiest scale. Looked at another way, it's the hardest. There are SO many ways of fingering it, it can be hard to achieve consistency and hence fluency. B major, however, has only one practical fingering, there are only two white notes, so those are where the thumbs MUST go. 'Pub pianists' (and possibly Irving Berlin, though I feel the story is exaggerated) are reputed to play in D♭ or G♭. There are less wrong notes if you stick to the black ones!
https://music.si.edu/object-day/irving-berlins-transposing-upright-piano
It's a bigger issue on guitar, where some characteristic 'licks' rely heavily on open strings. (But guitarists can re-tune or use a capo.)
Example: Chopin Scherzo #2, in B-flat minor. On the 11th page (sorry I don't have measure numbers - this is the 3rd page of the E major section), in the 7th and 8th measure of the running 8th notes in the right hand, we have G#6 F#6 D#6 A5 G#5 F#5 D#5 B4 D#5 C#5 B4 A4. (This is at about 90 dotted quarters per minute, so pretty fast.) This passage can be played at this speed because the long gaps land on white keys and are followed by a short distance to a black key, so it's easy to play the thumb under and move the hand over. If it was transposed by a half note either way, it would be much harder.
Key can affect playability, but it's not the case that any one key is globally more difficult than another.
Piano exams are a slightly different animal. The easiest levels tends to require chords, scales, and repertoire in keys with fewer accidentals — C major/A minor; G major/E minor; for example — because for beginners these can be easier to learn. But the repertoire is selected so that it's appropriately easy to play in those keys. More advanced repertoire might be quite difficult in those "simple" keys and easier to play in a "harder" key.
For the purposes of learning, the (not so) simple act of keeping track of which notes in the key signature are sharp or flat can present a significant difficulty, even with only one sharp or flat. Once one is proficient, however, this comes with relative ease, and the issues listed above become more important.
A thing that no-one has yet commented on is slide notes in jazz and blues. It is common to want to slide from b3 to 3 or from b5 to 5, and other slides are possible. This is done with one finger where possible, and from a black key to a white key. You hit the end of the black key and immediately fall off to the side onto the white key a semitone higher. If the relevant keys are not black to white then you can use two fingers, but it is harder to get that "bent note" sound. This means that some keys are easier for jazz and blues than others, if that bent sound it something you want. The only keys with both slides mentioned are C and G, which is weird because a lot of blues is in F and Bb. My guess is that that's a compromise with the Bb or Eb saxophone.
As a previous brass instrument musician I understand a bit about music. This seems like a comparison to playing a stringed instrument or using a typewriter/keyboard. Yes, some progressions would be easier to follow, requiring less dexterity.
With a stringed instrument you can add a capo (fretboard clamp) or detune individual strings to change the key but still use simple fingerings.
With a computer keyboard you can rearrange the button mapping so that more commonly used letters are closer to the center, to be more easily accessible. (as an aside for you younger folk, the layout of a mechanical typewriter was partly to reduce how far you have to reach for common letters, but also to reduce the chance that two letters tapped consecutively would cause the hammers to jam together at the paper)
As a whimsical conclusion, imagine designing a capo for or rearranging the strings on a mechanical piano!
As a professional accompanist who sight-reads for money, I often play the same piece in different keys. This is subjective, but I don't find that the key makes a difference in terms of playability. Some keys are definitely easier to read than others, however.
I just asked another pianist, and he confirms my answer.
