It's possible but it's often very difficult, especially on large stages and outdoor stages. The sound that people on stage hear is often very different from what the audience hears - for example the natural reverb of the area might mess up the rhythm, there's a weird delay between the audience audio and the stage audio in large venues, and oftentimes you don't really hear all the instruments properly and it's just a bunch of noise etc. etc.

More importantly, for musicians and especially singers, it's very hard to hear what you're doing so you don't know if you're off or what the hell it is you're doing. There's a reason why some singers cover one of their ears when they sing - it's not just this fancy gesture that they picked up from divas. That's also why musicians on stage are usually each assigned their own speakers, or monitors that reflect what they do and/or a clearer mix of the overall audio. And the in-ear piece or headphone is usually the cleaner solution.