Limit orders allow buying or selling stocks or options at a certain price or "better". Is there a way to enter or request that an order execute only at an exact price (for whatever reason)? If not, are there regulatory or other reasons why such an order cannot be entered?
No. (Or at least, "not today, not for retail/individual investors")
The Regulation National Market System (NMS) established by the Securities and Exchange Commission in 2005 was designed in part to help investor orders execute at a better price whenever possible.
The Order Protection Rule portion of the Regulation NSM mandates, among other things, that brokers route orders using the "most advantageous terms for the customer [..]"
So price improvement is effectively built into the requirement since it is "most advantageous".