It is a natural pattern of movements. Hunter-gatherer tribesmen squat ass-to-grass all the time to "sit". Chairs require effort to make and you risk insect bites if you sit on the ground, so they squat instead.
Since chairs require resource to make, they are usually reserved for people of authority while everyone else squat. That's how the term "chairman" becomes associated with position of authority.
Western cultures had largely abandoned squatting. While it may or may not be the primary cause, western-style sitting toilet (as opposed to squatting toilet common in Asia) means that Westerners rarely squat anymore, thus losing the ability to.
Now that we have established that ass-to-grass squat is natural, the next question is: should you?
Since this is Physical Fitness Stack Exchange, I'll focus on the sport perspective, more precisely, squatting with weight. However, I recommend also reading the effect of squatting on bowel movements. Long story short, squatting allows easier bowel movements compared to sitting.
First of all, are you a professional athlete? If you are, follow your coach's instructions. If you're not, then do what feels comfortable for you. Do not force yourself to imitate professional athletes. They know the risk of their sport and they likely had the talent or physical build to excel in it.
Then ask yourself, do I really need to squat ass-to-grass? Unless you're a professional athlete (or looking to compete), there is really no reason for you to squat ass-to-grass. Believe it or not, full squat is not universally superior compared to half or quarter squat. For example, this study found that quarter squat is better than full squat at increasing your vertical jump and sprints. If you just want to jump higher or run faster, there is no need to do full squat. This is significant because full squat is harder to recover from compared to quarter squat. A sprinter focusing on quarter squat will be able to train more often than one using full squat, without losing any benefits from squats.
Next question is, can I maintain proper posture while squatting ass-to-grass? Squatting is not just about depth, a lot of things need to go correctly. One frequent pitfall is your spine. Oftentimes the lumbar spine would round in the deepest portion of the squat. If you are using heavy weight, this could be dangerous. Only go as deep as you can maintain proper posture.
Finally, can I attain enough flexibility to properly squat ass-to-grass? It's easy to think that with enough stretching, you could be flexible enough, but sometimes flexibility issues rise not from the soft tissue, but from the bones. If you don't have the right bone structure, no amount of stretching would allow you to attain the flexibility required. This is important because if you don't squat ass-to-grass in your youth, your bones may develop in a way that doesn't allow you to, thus permanently losing the ability to do so.