I run a single chainring on my time trial bike, and until recently haven't bothered with a front mech or any sort of chain guide. However, since a recent upgrade to SRAM Rival cranks (with a Stages power meter) my chain dropped off the chainring twice during a time trial - when I was changing gear. To cure this, I could have fitted a front mech and all the cabling/lever that goes along with it - allowing me to get the chain back on without stopping.
To actually prevent the chain unshipping however (and to save all that un-necessary weight), I decided to custom-build a chain-stay that attaches to the front mech mounting points and is rigid. The photo shows what it looks like, fashioned from a sheet of 2mm stainless steel - involving lots of tough sawing, filing, hammering and drilling.
To demonstrate just how much the chain can flex when changing gear, here is a slo-mo video. Note that I did this under "no-load" conditions, ie, wheel spinning freely and turning the crank by hand, so it's probably a worst-case of chain flex. It's kind of scary just how much it wobbles left and right during the gear change: