It is well known that Institutional traders (Large trading firms, market makers) most of the time use LIMIT orders or Hidden limit orders. My question is, do they ever use market orders in their trading?
The short answer is yes but the way in which this happens is much more complicated so while eventually a market order is executed, it does not start as a market order. Big institutions often have large trades which cannot just be executed as a market order. They might even get in trouble with a regulator for moving the market if they aren't careful with such large orders. In fact, big firms, don't think of market or limit orders per se - they think of execution algos which are proprietary "orders". So an execution algo might use a market order. You certainly wouldn't use a market order on a $20 million trade because you'll swipe the order book and lose a lot of money purely on execution.
It seems to me that you are looking at such trading from the eyes of a retail investor? A market order makes a lot of sense for a retail investor and makes little sense for an institution.