Agree that it does not take much to get these animals to peak condition. There is a great deal of selective breeding involved with equines and dogs.
A bred for the task animal can rather quickly attain fitness given a proper diet, active lifestyle, and some buildup. There is value in doing some longer slower distance, tempo, intervals, hills, but you do not want to overdo it. Animals do not understand the reasons for doing a certain pace, and how to pace themselves for various distances/efforts. Specificity is key. Much of the training that does occur is done close to goal race pace.
With equines, you have to be careful about doing too many miles. They are big heavy animals and there is a lot of stress placed on their legs, joints and hooves. Must be careful on rough rocky terrain. This is especially true in training equines for longer trail races/rides. Its not natural for a horse to go 100 miles at high speeds.
Dogs are endurance machines, but even they can get sore paws and overuse injuries.
A problem with training some animals is they may run themselves into the ground with exhaustion, injury, inflammation, etc. They can not tell you something is sore or aching, and will just go on it until it becomes a major or serious issue. Another good reason to be conservative in training.
A big issue with some animals is their long term motivation and incentive. Long intensive training, especially over weeks and months, takes effort. You risk burning animals out mentally with too much training so they may only be good for a few good races. They may still run fast once they are 'over it', but they will never be at 100% again.