I do think controlling a small car with 5 people in it (or more) is very different to controlling a more powerful car with only yourself and 1 passenger in it for lots of reasons. Perhaps learners could be encouraged to have lessons with other people in the car, to help them understand how the weight and behaviour of passengers makes driving harder.
I also think that non-driving friends make the worst passengers for new drivers. Other drivers often know when to be quiet and let the driver concentrate, whereas non-drivers just won't realise when a situation is more difficult/dangerous.
However, I also think that if you passed this law, it would have to apply to all drivers, regardless of age- are 3 distracting children really that much less of a danger than three distracting teens?
It also sounds like this crash may have been caused by someone else's poor driving. I do think mandatory retests- perhaps one after 5 years and then one every 10 years could help keep people driving more safely, and maybe have enforcement cameras looking for all bad driving, not just speeding. There should also be a limit on the number of tests you can take- one girl I knew failed her test 7 times before passing on the 8th attempt. I doubt she was really a safe driver when she passed.
There is also a stretch of road near me where teenagers occasionally drive too fast and crash- luckily most of them walk away, but some don't. However, lots of older people do crash their too. Really, the road is no longer suitable for the volume of traffic driving on it, and should be improved to make it safer, but this would be expensive and so is unlikely to happen.