Is there a time period when they actually use "1" instead of "A"? or is that just as per what the designer likes?
The Ace as an "A" rather than being simply a "1" came about in the days following the French Revolution of the 18th Century. There were a number of changes that took place to the Parisian playing card design - when the royalty were overthrown, the King, Queen and Jack (Roi, Dame et Valet) were replaced with Liberty, Equality and Fraternity (Liberté, Egalité et Fraternité) and the 1 was replaced with the Ace, now the highest ranked card, representing the power of the people once thought to be powerless. While royalty did eventually return to the Parisian deck, the concept of the Ace remained and eventually became used as it is today, as either a high card or a low card (or both at once) depending on the game being played.
While most French decks use an Ace these days, some still use the traditional pre-Revolution 1 for the card's index. The most recent French deck I know of still using a 1 would be at least one of the Anne Stokes/Alchemy decks made by USPC.