'Safe Mode' is also called 'limp mode'. Its a mode that stops any action damaging the engine by limiting your speed.

Sometimes by turning the engine off, and back on again it goes back into normal mode, but you really should get it checked out as there is something serious regarding the engine.

"luckily I was able to coast to the hard shoulder without hitting anything".

There's no luck about it, anything else would be operator ineptiude. Losing power on a motorway is not pleasant, but it is not a cause for panic. You have plenty of momentum to get from lane three to the hard shoulder.

A few years ago when I had an Accord I was pulling out onto a roundabout when it suddenly went into limp mode - it wouldn't do more than 20 mph. Luckily there was no immediate traffic

This is rather less pleasant. But ultimately, unless your manoeuvre was a rash one, other traffic on the roundabout should be able to cope without an accident (although there may be some horn blaring and gesticulating). It's no more of a hazard than stalling a car. People don't consider themselves a danger to the road and report themselves to VOSA if they stall at a roundabout, do they?

You cannot take mechanical reliability as a certainty. There are many reasons for an engine to stop dead, and your driving must reflect this!

Limp home mode allows an engine that might have a serious fault, to be have limited operation to allow the vehicle to be moved, say to a garage. It's a jolly good thing.

I've driven a number of cars when "Limp home" cut in ("Fail Safe Mode" is the technical term).

Each time I was driving on a dual-carriageway and each time I was able to quickly adjust for the sudden power lose, not so easy when one car had black smoke pouring out of the exhaust with intermittent drastic power loss.

On another occasion (many years ago) when I was passing a lorry on yet another dual-carriageway (night time unlit road) the fuel relay blew resulting in zero power. I turned on the hazards and then indicated to move to the left lane to let the lorry know I was in trouble. I had declutched to reduce engine/transmission drag and had just enough forward motion to move to the inside lane when I saw right in front of me an empty lay-by where I was able to safely pull in. Opposite side of the road was a cafe' which was about to close, they looked after us whilst we waited for the breakdown service to arrive about 35 mins later. Car was carried back to our local garage and we were taken home, it was mid-winter and dark when this happened.

Someone was definitely looking me on each occasion that’s for sure.