Finally, one can also make a case for one engine being more reliable than two engines. With the same failure rate per engine, two engines = twice as many failure per unit service time. While having two engines gives the aircraft limp home power with some failure modes, others will render the aircraft inoperable even if it originated from only one of two engines -- a runaway fire, blade out damaging the adjacent engine or fuel tanks, etc. Basically, any kind of engine failure that renders a singe engined aircraft unglidable also renders the two engine safety net moot. A larger engine is more resistant to certain events like bird ingestion.
Actually I think that is a plausible argument but it has a limitation for single engined aircraft where your effectively trading redundancy for reliability. One of the arguments for twin transtlantic commercial airliners apart from greater operating efficiency was that an equivelent 4 engined aircraft would have twice the chance of an engine failure which would result in it having to divert immediately. The difference here is that unlike the twin jet that had redundancy in that it could fly on one remaining engine, the F-35 would more than likely be lost if it had an engine malfunction.
Its true that a lot of causes of engine failure would result in more or all of the engines failing on a multi engine aircraft but likewise there are many causes that would just cause the one engine to fail. You mentioned one which was bird/debris ingestion which is rare to occur in more than one engine at a given time. Also you mentioned damage caused by the failing to adjacent engines/systems, I know that modern civil turbofans have kevlar shielding to contain and protect vital systems and areas of the aircraft in the event of a blade out. I would have thought an advanced combat aircraft would have something similar.
I totally agree with the increased reliability with a single engine but you do sacrifice the redundancy you get with two engines. At least a twin engined aircraft that has lost an engine can limp back and be used another day (if nothing else major has packed in).