Cannot fix pedal into crank spindle hole: what is the appropriate repair?

Presumably the repair person was a bike shop, not a machinist. They'd rather sell you new parts and fit them - it would take less time.

Installing a "helicoil" or thread insert is not hard, but your chances are improved with better tools. A hand drill will not be enough, you'd need a pillar drill at a minimum.

A thread repair kit itself for pedals is surprisingly expensive, because 9/16" left and right hand threads at 20 TPI is an oddball size. The common industrial number is 18TPI and those will not fit your pedal's axles. Expect to pay hundreds of eurodollarpounds for an 8~10 piece kit, for each handed thread.

The axis of the hole you drill must be absolutely parallel to the bottom bracket. Otherwise any misalignment will be felt through the foot on that side.

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Depending on the damage, you might get away with simply re-tapping the hole in the crank, though if you're talking inserts then the damage has gone further.

It might be worth exploring for a replacement crank from a donor bike too, rather than buying new.

Pedal thread helicoils do not fall out while riding. It is a very safe repair. The one thing that can keep it from being safe would be if too much material has been lost, such that the new threads cannot be fully formed. The crank is done if that's true, but that's not usually the situation and does not appear to be true of your crank.

The whole procedure to install a pedal thread helicoil takes maybe 30 minutes for an experienced mechanic including all the cleanup and getting the crank on and off. Getting the alignment square when you're starting to cut the new threads and trimming down the insert to look neat are both steps that take some time and care. The part costs something as well. For a right crank, even a basic one, it is still usually cheaper than a new crankset plus installation labor, and that's if a new crank can necessarily be had that can use the existing bottom bracket. For left cranks from basic low-end cranksets, just putting on a new left crank is almost always cheaper if one is available, but even there is the fact that a good match might not always be available.

If a crank has significantly worn chainrings, it's easy for it to be the case that a whole new crank is a better value. The catch there can be that even if it's a better value in the overall sense, dropping in a new crank in a worn out drivetrain is problematic, i.e. a customer who needs a new drivetrain but wasn't planning on being confronted with the fact.

Not every shop really does crank helicoils but many do a lot of them. Some people basically just don't get the physics of how they work and why they're safe, unfortunately including some mechanics. The tool to install them is also fairly expensive.