Why isn't the upper limit of pain lower in humans?
You are assuming that fighting back with a bad wound would be more useful than dropping to the ground. That is not always the case.

Dropping to the ground and ceasing activity is very adaptive in almost any situation involving potentially significant blood loss. Becoming prone or supine prevents loss of consciousness, the most critical aspect of survival. Decreased movement is also likely to decrease the rate of blood loss (though not in as significant a manner as consciousness).

Certainly with a significant abdominal wound, running would increase cardiac output, which would increase bleeding. Is running from a traumatic event advantageous if you pass out before escaping? On the other hand, lying prone and holding the wound (instinctive) may reduce bleeding and prolong consciousness and life.

What "cannot be helped" (like withdrawing a hand from a flame) is usually advantageous.

An infant's cry changes during circumcision (an involuntary reaction to pain). The cry in turn naturally produces a visceral reaction in nearby adults that compels action (causes a state of strong sympathetic nervous system activation.) The adult either avoids the cry by trying to distance themself, or responds by coming to the infant's cry.

The infant cannot help changing the intensity of the cry with intense pain. If a "certain level of pain" was as far as one could feel, the baby might not elicit the sense of urgency in adults which it does.

Newborn pain cries and vagal tone: parallel changes in response to circumcision.
ASSESSMENT OF INFANT CRY: ACOUSTIC CRY ANALYSIS AND PARENTAL PERCEPTION