Surely it would be incredibly subjective to require a definition?
Whereas in Scrabble as it stands, a move is either legal or illegal. It's very black and white. Well, once you decide on the dictionary you're playing to!
I stopped playing Scrabble against my father because he was frustrated that I had memorised every two and three letter word. Even being able to define many didn't matter; if they came across as though they were memorised rather than learnt, he was annoyed. I don't see the issue. Everyone who plays is playing by the same rules.
A common thing is to give all players a list of all of the weird little 2 and 3 letter words. The problem with them is not that they're illegal, just that knowing them is very gamey unfun busywork, but gives a big advantage to everybody who spent time memorizing them.
Wouldn't that significantly cut down on the valid moves possible from a given board configuration? You'd only be able to play perpendicular to preexisting words.
I imagine that the parent considered that one could play a longer word that happened to make shorter words just not _only_ play a two letter word; so parallel words would be acceptable as would things like in-fills that only took one letter but caused 2 words to be formed.
Perhaps a better, succinct, rule that tackles the same problem would be "a minimum of two tiles must be placed".
You're right, I didn't think of that - but if you're playing with someone who doesn't know too many two-letter-words, that might come up less frequently anyway.
Having played a lot of Scrabble with my wife I can feel for your father a bit. I think its probably less about having memorised them, and more about two players of dramatically different skill levels playing the same game.
Eventually I came to terms with it and just considered anything within a two hundred points or so of my wife's score as a personal win, but it can still be frustrating to feel you're playing your best and losing to someone who's barely trying.
The moral of this story I think is not to play an English graduate at Scrabble unless you're OK with losing.
And it makes the training less pointless. Words without meaning are useful for nothing besides winning Scrabble, knowing strange words WITH meaning however has a chance to be useful outside the game.
But actually that'd be a fun variant.
A spelling bee where you choose the word based on the constraints of scrabble.