An engine failure requires land at the nearest suitable airport which is why distance is important.
I'd always thought that takeoff altn' within 60mins was for the 'land at nearest suitable' and that can be for more than an engine failure on a 'twin'. (remember the 3 engine flight on a 4 donk a/c much debated on here) In a twin, if you are non-ETPS, do you not need to remain within 1hr of a suitable airfield. Is this not where the 60min rule comes from? In the event of other systems failure one might consider an airfield, even destination, as most suitable.
A non engine related problem might be departing with APU u/s and then losing another source of AC = 1 source only.