I could give you an answer, but that would be pure speculation. Since the IAAF era began in 1912, the mile record has dropped by over 31 seconds. That's an average of about one second every three years. As of today, the record stands at 3:43.13 and has not been broken in 2885 days. This would seem to be a long time unless you realize that in the 95 years since the IAAF era began, there have been 4 even longer periods than this current one without a change in the mile world record: periods of 2960, 2962, 2964 and 3215 days. The longest stale period was the nearly 9 years between Gunder Hagg's 4:01.3 and Roger Bannister's inconceivable 3:59.4. Can the record drop another 31.27 records over the next century like it did this past century? That seems as impossible as Bannister's sub 4, doesn't it? "Second question: are records often unofficially (or unknowingly) broken during training? Or do athletes save their best performances for sanctioned events?"
I've heard of it happening in cycling, but I'd have to imagine that the vast majority of athletes, including cyclists, would want to test themselves in competition against others, rather than languish in obscurity. Once before the 1972 Olympics Games in Munich, Oregon coach Bill Dellinger had the legendary Steve Prefontaine run a 3:59 mile all by himself in training, just "for sharpening." Pre, of course, was the exception to just about every rule and was incapable of languishing in obscurity. Most athletes would heed the advice of Thomas Gray, who said that, "full many a flower is born to blush unseen, and waste its sweetness on the desert air."