Whereas you might tame all sorts of beasts in varying quantaties to reach your goal, in between training you can break the monotony by going out and hunting with pets appropriate to your skill level. It can be as much or more fun even than going high end. Thats where you learn your trade as a tamer.
Sorry, but you're deluded if you think any significant quantity of people go hunting with a bunch of harts, mongbats and cougars as they're training the skill. Taming, along with many other skills, is only useful at the highest levels if you want to kill anything more challenging than lizardmen so people generally powergame up to that standard or do so with jewellery to play the real game.
In any event, assuming that isn't the case for a moment, killing lizardman with polar bears doesn't teach you anything about actual end-game encounters so the point is moot. What Titans1 and you describe is what /should/ happen ideally; I absolutely won't dispute that. It just doesn't for a variety of reasons, such as the skill gain system being rather archaic and uninspiring, a lack of meaningful mobs to kill with weak low-end pets that do not result in meaningful progress for your character through taming gains and most players being veterans these days who'd rather buy a mystic token than put themselves through the monotonous grind that they know lies ahead.
If there was a quest (even a once-a-day repeatable one) that asks you to tame X mob (let's for the sake of argument say an ostard, but this would vary depending on your skill level at the time) and kill Y number of monsters which would be challenging for the pet and your general skill levels (10x imps, perhaps in a specific place too such as Blood Dungeon) which will reward 5.0 taming skill when you turn it in this would encourage more actual play and learning than the system we have now and make some of the most grindy skills a whole lot less boring and repetitive to train. It would give less reason to want to use scripts or other types of automation too, since actually playing the game would be quicker.