At the varsity level, you get about 1-2 seconds from when your opponent hits until you have to hit. That isn't very long, but the 20 feet you may need to run also isn't that far. In fact, you can all jog 20 feet in 2 second no problem.
But, what if it takes you a full second to start running? Now you have to run 20 feet in 1 second. That's nearly 14mph.
Remember, your goal is also to stop running and get set and balanced to hit. That's possible if you got moving quickly, but practically impossible if it took you close to a second to start running and you are only getting to the ball at a full sprint.
Footwork drills exist to help you start running sooner - about a 1/4 second to a 1/2 second after your opponent has hit and you know where you need to run. That quicker start is a HUGE advantage. It gives you:
More shots that you can get to (probably worth 5-10 point a match)
More time to get set and hit (probably at least another 5-10 points a match)
Forces your opponents to try to hit harder or closer to the lines, causing them to miss (possibly another 5-10 points a match).
To win a set, you only need to win 24 points. Getting 15 or 30 extra points that you win just by being quick is massive. Simona Halep easily defeated Serena Williams in the 2019 Wimbledon final with speed (it didn't even take an hour!!!). Check out this video:
Notice how many times Halep's quickness kept her in points (#1 from above). By the end, you can see that Serena just starts to miss a lot. She couldn't get it by Halep, so she tried to hit too hard and/or with too much angle (#3 above) and misses.
Here are some things to help make you quicker:
#1: Learn to split step and do it every time your opponents hit. Every time. Even in practice. Especially in practice. It has to become a habit that you just do. How important is this? So important that I made some low-budget YouTube videos to help you practice at home. The second video is a little over 5 minutes, which seems to be a good amount of time to work on this. I would guess that someone who does this for 5 minutes 2-3 times a week then works on split steps in practice will improve their chances of making varsity by 25% over someone who doesn't.
Video 1: How To Use Video 2.
Video 2: 5 Minutes of split step practice. Unlike me in the video above, practice this somewhere where you have room to push off and accelerate out of your split step. Here it is:
#2: Get quicker feet, better balance and more strength to push off by doing hexagon and ladder drills. For these, I'd recommend making your own hexagon and ladder out of tape or chalk (it's cheaper and easier). The specs are below for how to draw them.
Hexagon Drill: Two times around, always facing one direction. Video below:
Agility Ladder Options: This video has a wide variety of things to practice from beginner through advanced. Start with the easier ones. Video below:
You can also search YouTube for tons of other agility ladder drills, some of which get very complicated.
Build your own agility ladder and hexagon with the diagrams below.