It also affects the way that races set up - if you don't care about time all you have to do is train for the cruise and finishing kick (like Olympic races rather than rabbited WR attempts in athletics terms).
Lack of time bonuses mean that a horse who is winning easily (which is also a horse likely to be close to a WR) isn't going to be "ridden out" fully (which is also why more than half of the recognised WRs have been set in claiming races - which are the equine equivalent of the local 5k). Any jockey who rode a horse out when winning by 10 lengths would be immediately sacked by the trainer, because it (a) to do so would exponentially increase the risk of injury, and (b) make the horse's recovery that much longer (if the jockey "wraps him up" when the race is won, the horse might be able to race again in 10 days versus a month to six weeks if the horse is ridden to exhaustion chasing a meaningless time - I can remember that when Elliot Walden won the Belmont with Victory Gallop, he put up his "day rate" for a horse in his stable to $300+ - that alone is an incentive to race as frequently as possible).
One point about the training, and why horses don't benefit from training like humans; horses carry a "reservoir" of around 30% of their total volume of red blood cells in their spleen, which is released by the fight or flight mechanism (adrenalin). This ability isn't actually "trainable", but it does help to explain why horse races set up the way they do. The longer the horse can "cruise" without going into oxygen debt means more energy saved for the "kick" which carries you clear of your rivals. It also, IMO, explains the high injury rate in racehorses, since, in full "race mode" their muscular system puts out far more power than their tendons/ligaments/bones are used to handling - resulting in a highly increased likelihood of breakdown if they take a funny step, or get bumped, or step in a hole.
The problem is that you can't train to activate that system a little bit, it is an on/off switch, not a gradual release (you'd have to sit on a real racehorse going at full speed to understand), and if you activate the system too often you are going to "sour" the horse and he won't want to run.
Interestingly, Graham Motion, the trainer of Animal Kingdom, trains his horses at Fair Hill in Maryland, and I know he sends the young horses out to trot and canter on the trails in the parkland around the training center as much as he possibly can. I don't know if he has a better or worse injury record than other trainers, but it certainly seems to be working for him in terms of results.
One final point about Tom Ivers - he talks a good game about how trainers should use interval training etc., but at the end of the day Ivers has been in the business for 20-30 years and never won anything better than a claiming race. If results speak louder than words, then Ivers should definitely shut up!