Why does the incentive compatibility constraint bind (moral hazard)? Consider a very basic model of moral hazard with two possible effort levels $e_L&lt;e_H$ and two possible levels of output $y_L&lt;y_H$. If the agent doesn't participate, they get utility of $\bar{u}$. If they participate, they get $E[u(w)|e]-c(e)$ where $u'(w) &gt; 0$, $u''(w) &lt; 0$ and $c(e_L)&lt;c(e_L)$. In other words, the agent is risk averse and dislikes effort. Putting in more effort raises the chance that output is high, i.e. $P(y=y_H)=p$ if $e=e_H$ and $P(y=y_H)=q$ if $e=e_L$ where $1&gt;p&gt;q&gt;0$. The principal chooses a contract ${w_H, w_L}$ which specifies a wage following $y=y_H$ and $y=y_L$ respectively. Since they are risk neutral, they choose $w_H$ and $w_L$ to maximise $E[y - w]$.

Let us suppose that the principal wishes to induce $e=e_H$.

The optimal contract must satisfy an 'incentive compatibility' constraint:

$$pu(w_H)+(1-p)u(w_L)-e_H\geq qu(w_H)+(1-q)u(w_L)-e_L$$

In the optimal contract, this must hold with equality ('bind'). If I recall correctly, this has something to do with optimal risk sharing (more precisely, that the principal doesn't want to expose the agent to `unnecessary' risk). However, I would be very grateful if anyone could provide a more precise (but ideally still intuitive) explanation for why this must be the case.
The idea behind the incentive compatibility constraint is that the expected utility when doing the high effort level needs to be as least as large as the one the agent would obtain from doing the low effort level. There are many contracts that satisfy the IC. Given that the agent is risk averse, i.e., has strictly convex indiference curves, the further the asymmetric information contract deviates from the symmetric information contract, the higher will be the expected payoff the agent receives. Of course, the higher the expected payoff for the agent, the lower the expected payoff for the principal. Hence, the principal will choose that contract that a) provides the agent with just her reservation utility and b) the IC is satisfied as an equality.

Perhaps what you have in mind is that, since the expected utility for the agent is the same irrespective of the effort level she exerts, she may as well end up doing the low effort level anyway. But recall that the agent is indifferent between the two effort levels, and, therefore, we can assume that she chooses to do the high effort level.