"As for standardising training for pilots, I’ve had three aircraft on top of each other 1000’ apart approaching weather. One requests left 10, the next 15 right and the third says nothing. Surely it’s best to all do the same thing, even if in the captain’s view it’s the less good (2nd) option?"
Standard training for pilots for weather would be fine if there was standard weather. It does't work like that. Cells shapes are often very irregular and very dynamic in that they can grow rapidly, in different directions, right in front of your eyes. Interpreting these shapes visually can lead to different decisions and this can all happen quickly. You can fly through a 40,000' CB without a ripple and get absolutely battered by an 8,000' cell. Equally you can make a judgment call, with the best intentions and need to change it a minute later.
The following video is obviously not in real time but you can get the idea why sequential flights might want different courses:
https://www.videoblocks.com/video/to...er-day-aqbcnje
In an ideal world pilots would be able to make early decisions and pass these promptly to ATC and everyone could come up with a timely, workable, agreed plan. But there are days where that just doesn't work.
Regarding the weather radar, manufacturers and subsequently many aviation authorities overestimate the accuracy of their products. While they are very useful tools, and they have improved slowly over the years, they should not be relied upon exclusively. The resolution used for aviation weather radars is only really useful for rain and wet snow. Even on max settings they are very poor at detecting dry hail or any icing. As has been pointed out here, and it in the US AIM, ATC wx radars do not show turbulence but most aircraft radars do. These can also pretty poor as they frequently lead you happily down a path and then suddenly give a strong indication of turbulence right in front of you. Very often when your eyes get a clear view of the weather you will reject what the radar is showing you. Experience in these scenarios is invaluable.
Also, some people here seem to forget that there are passengers on board. The bigger the aircraft, the more nervous passengers you are likely to have on board and they can really freak out in the turbulence associated with flying into a cell. While pilots, cabin crew and most passengers will be fine with the roller coaster ride, crews have to think of their customers. Imagine throwing a medical emergency, due to anxiety or whatever, into the mix in that recording!
Finally, I must compliment the NY ATC people as usually they are excellent in assisting with bad weather requests. But personally I would be disappointed with the service in that recording.