Totally agree. We have a mix of algorithmic/automated monitor and visual monitors. I can tell you a lot more about how healthy our site is from looking at two screens in our NOC than I can from all the pages sent over the last <pick your time range>.
Computers are great at executing repetitive, specified tasks. Use them for that.
Humans are great at pattern recognition and flexibly adapting. Use them for that, IMO.
I still use pushes for clear-cut things that require paging, but having graphes of a lot of things and just noticing changes or anomaly on the overall patterns will help spot a lot of issues, including things you haven't yet planned paging for :-)