I think if you omit that behavior of aces, many people who are used to blackjack are going to be unpleasantly surprised when they bust unexpectedly.
If, in the course of designing more cards for the deckbuilding aspects of this, you decide to have cards that are always 11 and never 1, or for that matter always 1 and never 11, I’d suggest labeling those cards “11” and “1” rather than “A”; if you present something as an ace, people will expect it to behave like an ace.
I’d definitely suggest providing aces with the standard ace behavior, though; in the course of a blackjack deckbuilder I think you’ll want lots of cards with values that change for various reasons.