Switching off is much safer than a turbine overspeed past certain limits. Because an engine failure (one engine) is a situation all pilots are trained for and it has an almost certain safe outcome. Airplanes fly and land just fine on a single engine. We all train for engine failures all the time.

On the other hand, a runaway engine fire or uncontained turbine failure is much much more likely to cause a crash.

So almost all jet engines are designed to have a shutdown (sometimes helped by the built-in fire extinguishers) as a worst case outcome. The quick response drill for an engine overspeed or temperature past certain limits is to shut it down immediately and pull the fire extinguisher handle.

But why not throttling instead of switching off then?

Good question, you could theoretically throttle a runaway engine by reducing fuel flow (unlike a piston engine where you can limit air intake). But in 9 out of 10 cases you've already done that by pulling back the power levers. The next step is to cut off the fuel, because the throttles didn't get it under control.

Overspeed protection takes place once everything else has failed. The engine controls have already attempted to throttle down and such. If that doesn't work then overspeed kicks in.

Adding on to this... things inside an engine happen FAST. Too much energy can spin up the turbines to the point of failure in milliseconds.

Yep, as anyone who has ruined a fan by shooting a canned air duster at it can attest. :(

I think almost every plane can glide safely for a lot longer than it takes to restart the engines. Could be dangerous at low altitudes still.

That and restarting an engine in-flight is faster than starting it on the ground because it's already spinning (by virtue of sailing through the air, like a windmill). This is, aptly, called windmill starting.

You would be surprised at just how safe and 'normal' shutting off the engines on a plane is.

Related, British Airways Flight 268, a B-747, when taking off from LAX had a problem with one of it's engines so they shut it off, and continued flying all the way to London, albeit to Manchester instead of Heathrow, with one less engine. https://en.wikipedia.org/wiki/British_Airways_Flight_268

Shutting down one engine is one thing. Shutting down all engines is what surprised me.

that's why this is news. it's very rare.