If restaurants really cared about fast service, they would hire more staff.

You are missing an important part of the equation; restaurants care about fast service in relation to affordability and profit. They could definitely hire enough waiters and chefs so that every table had a waiter and cook dedicated to just their order.

The problem is that this staff likes to get paid. In order to hire sufficient staff for the above hypothetical, the restaurant would need to raise the price of the meals sufficiently enough to cover the wages of said staff. The result of doing so would be meals so exorbitantly priced, that no customers would be willing to actually patronize the establishment, and the restaurant would close down.

There is a happy medium that provides sufficiently fast food on average while also not forcing prices up unreasonably. The problem is that on average; it is impossible to know beforehand exactly how many people are going to attend the restaurant at any given time on any given night. A manager needs to estimate how busy their business will be, and staff appropriately. Sometimes a night ends up being busier than expected, and as a result there is insufficient staff to be able to provide the "fast service" that you are looking for.

The same holds true for fast food restaurants; they could install enough registers so that there are never more than 3 people in any line at any given time, and enough people staffed to attend every till and cook every meal immediately. But the consequential increase in cost (due to increased rent - the restaurant would need to be bigger to account for all of the extra tills, increased wages for all the extra staff, etc.) would quickly run the restaurant out of business.

In brief, if you really want to have a restaurant quality meal without the wait, start scheduling your meals for times different than the norm; Have 4am breakfasts, 11am lunches, and 4pm dinners, and you shouldn't have too much of an issue with lines.