Sensation is information
The culture has historically taught otherwise.
A great deal of instruction in this field frames discomfort as something to breathe through, to soften into, or to observe without reacting. As a way of relating to ordinary muscular effort that is reasonable. Applied indiscriminately it teaches people to ignore precisely the signal that prevents injury.
The distinction worth teaching is between broad muscular stretch sensation, which is generally fine, and sharp, electrical, or joint-line sensation, which is not and should stop the position immediately. Most people can tell the difference once it is named.
The same applies to the following day. Some soreness after unfamiliar movement is normal; pain that is worse the next morning, localised to a joint, or accompanied by any loss of function is not, and is worth attention rather than another class.
This is one of the areas where the culture of a class matters most. A room in which nobody ever comes out of a position early is a room where people are ignoring information, and the norm is set by the teacher.
It is worth adding that the timing of sensation matters as well as its quality. Discomfort that appears immediately on entering a position is different from discomfort that builds after thirty seconds, and the first is far more likely to indicate that the position is wrong for this body rather than merely demanding.