Going to a Mysore class on a regular basis I have the opportunity to see how others practice. I am focused on myself, but from time to time I realize the practice of others......and I see "mistakes". Why to practice correctly? Isn't it enough to have fun???? Doing anything is better than doing nothing, isn't it?
In some cases doing asanas not correctly can lead to injuries either at once or on the long run. A typical example is urdhva dhanurasana. It seems to be easier to drop back with feet and knees pointing outwards. But this is again the natural movement of the joint. I don't drop back anymore for this reason. Again I think that it was not a good idea to make this pose to an entrance ticket for being allowed to do second series.
In some cases it is simply much more difficult to do an asana when doing it not correctly. And example is sirsasana (headstand). When the elbows are too far away the pose becomes instable, almost impossible. Knowing how to do it correctly helps to learn the pose I'd say in a week.
Otherwise, yeah it is possible to practice incorrectly, but then I do not get the most out of the practice: An example are the strong legs. I was told to engage the legs during the standing sequence. This makes the asanas more stable, but prepares myself for the second series, where much more strength is necessary than in the first series.
Practicing correctly I get what I want faster: strength and flexibility, a relaxed mind.
And it is endless. The only goal can be to establish a daily practice and to do what is possible on that day.