You have to standardize on some common granularity for strikes/expiration dates so that each symbol has sufficient volume so that the market would not get too sparse. The theory does not require it, but when you are building an exchange, I suppose that'd be of a practical concern to you. You want interchangeability in derivative contracts and don't want each individual contract to be a snowflake.

There are "mini" options that control 10 shares, for example, but they usually have higher bid-ask spread reflecting the higher cost of pricing accurately/transaction fee/lower liquidity.