When you imagine how it feels when someone is doing yoga, you will usually imagine them as in the pose, standing barefoot on one leg, but the view has changed recently because of several reasons. Some of the reasons are health problems, and performance-based.
When dealing with yoga, you have to learn and practice for it to be very effective. Some people do this at home, but the greater majority of learning and practicing yoga in public places, such as a gym or yoga class. You can get a good-quality yoga shoes from various online stores.
When you do this, you will usually be assigned your own mat, where it will take place. These mats are usually cleaned, but not always, and not always as good as they should be.
For the same reason you do not walk barefoot in everyday life, the same applies to why it was probably not a good idea to be barefoot on the mat. Not to mention that not all of the time you will be on the mat. You will definitely have a time where you dropped it.
That is why more and more people are starting to use some kind of foot protection when doing yoga. This works great in keeping your feet clean and safe but also can improve your flexibility by giving you more support during your poses and gives you a better overall workout.