What's "hard" is:
An airport that is "nearest" in straight-line distance may not be "nearest" in time.
An airport that may be "suitable" may be marginally so.
A "diversion" at TOD may cause significant additional safety risk to many other airplanes and people as ATC tries to reshuffle traffic to accommodate your emergency. Priority handling on the anticipated arrival to your original destination will cause much less disruption. Fuel contamination (the other major cause of multiple engine failure besides fuel starvation) is unlikely near the end of the flight if there are no indications (e.g., Filter Bypass warning) prior to the first engine failure.
An interruption to normal routine always carries additional risk. It is up to the Captain to decide how much additional risk is appropriate for the situation, and to balance offsetting risks.