Meh. I say go for it.
The only thing major it does is increase their power - which is something only the DM needs to worry about. It doesn't change the game (aside from such situations with the warlock and such - but 5e is already a relatively "un-balanced" game as is*) and the CR system is not all that precise.
Since the DM will always need to assess each encounter with regards to his players, that you now have more powerful characters than they "should" be changes... well, nothing.
Case in point : magical items are not assumed.
The point about character building choice being a part of the game is true only insofar as the players like that part of the game (to a certain extent, of course.) I see little value in trying to "educate" these players into the "correct" way of looking at character progression rules - if they already feel as if choosing a feat would "rob" them of something, that feeling isn't going to just go away. The effort required to change perceptions can be immense - it might not be, but if it is, I'd say this is not a battle worth picking.
*I say "un-balanced" with quotes to mean that to have what could be called IMO strict balance requires a very specific game (a fairly set number of encounters between rests -both short and long-, a mix of encounter types tailored to the PCs, a mix of combat encounter types tailored to the PCs, etc, etc.) If these pretty narrow margins are not obeyed, the relative balance between the characters will not be equal. This, in no way, shape, or form, equates to the game being broken or some such. It simply means that specific character classes and builds would have a variance of impact on the game. A simple and exagereted example could be a party with multiple clerics in a political campaign centered around different faith's power plays and massive undead presence. The clerics could easily hog the spotlight.