I would disagree, you still have the build time. And even if engineer doesn't do anything during that time, they are still occupied. No one would switch tasks during 10 minute build, there's just nothing you can do during such a short timeframe. In that case, in terms of business costs, it doesn't matter if engineer is busy or not during that period: they are still not gonna be doing more.
The alternative to spending X minutes waiting for a CI build is spending slightly more than X minutes executing a manual build with a nonzero chance of time-wasting mistakes, not doing nothing.
Not waiting for a build means not testing it, in which case a manual non-build of an uninteresting software configuration seems attractively elegant but a CI system still provides value by recording that a certain configuration compiles and by making the built application available for later use in case it's needed.
That is indeed true, CI is way less error prone, thanks. Having a build ready to go is quite handy too.
What do you mean by "not testing it" "seems attractively elegant"? Testing a build is still a must, although that ends up to be manual testing usually (unit tests don't assure much, integration take a lot of engineering effort for setting up and writing, especially if they were not taken care of from the start).