Each employee has a hiring fee, so hiring and firing very often will cost you extra money. There's something to be said for not replacing your employees 'too' often. I.e. if the recruitment cost is $2500, the new employee is 10% better, then you need to consider the time it takes them to earn $25,000 as the ROI for the decision. Having your hiring cycle be quicker than that will actively hurt you even if you improve your staff.
Apart from bonuses gained from training in the Training room (up to 5-star level for up to 5 abilities learnt) as well as a per-level bonus to most relevant skills in general there's no additional benefit to keeping employees for longer.
Why is the information useful then?
The reason the game seemingly keeps track of this is for you to gauge the profitability of the employee. To imagine the usefulness of this imagine that there's three people you could fire and replace with the newer person (who has better traits), but you don't know which of the three has worse traits. Say your new GP doctor has 'happiness +10%' and your old GP doctors have 'lazy' and 'needs to go to the toilet more often', and 'slower walking speed by 20%'.
E.g. you can try firing each one of 3 different employees that would be a good fit for being replaced, and only fire the one with the worst stats in the panel, the goal is to sort them by;
where P is patients served and t is time served to find the employee who managed serve the most patients per unit time to help you decide which to keep.