Some engines can be restarted pretty close to instantly. Depends on why/how it stopped running.
And no, it doesnt always do nasty things.
A true story - Richard Bong, while flying his P38 in a fight against Zeros, noticed a Zero going after another P38, with damage obvious. Bong shut down one engine, flew as to distract the Zero, after the Zero made a pass on Bong, he fired up the dead engine, engaged and killed the Zero.
Didn't take him a long time to restart it.
Dont push for something if you have no idea if it is historically and operationally correct. A windmilling engine only needs fuel and ignition to run, shutting it down in flight in a hurry would only take about a second or two, turning back on the fuel or igntion again would only take about the same amount of time. In a combat situation a pilot could have it up and at power very fast. In the civilian world when starting up an engine in flight, its more common to let it warm up at idle for a short time to avoid thermal stress.
How about we dont sweat the small stuff and instead hope that HTC works on new versions and significant improvements?
Dago