That works so long as the build script is just doing a linear series of things. But if it's anything remotely modern then a bunch of stuff is going on in parallel, and if all the output is being funneled to a single log, you can end up with a fair bit of wind-down spew you have to scroll through to find the real/initial failure.

How much better would it be if the CI web client could just say, here's everything the build tool built, with their individual logs, and here's a direct link to the one that failed, which canceled everything else?