What happens if you don't have horses? Do you just quit right then? Multi-move units arent' as good as they were, and if the AI was at all competent on city defense (i.e. if it ever put more than three non-conscripts on a front-line city to go against your 20+ cavalry stack of doom), your blitzkrieg strategy could be easily foiled, at least until modern armor (equal numbers of fortified mech infantry will most always win over tanks, and rifleman or better will almost always take out more than their number in cavalry). And what happens if there are hills/mountains or 3+ tiles along the nearest path to the next enemy city? Aren't those mobile units just as much sitting ducks as unmounted troops are?
What's your solution to taking down size 20+ AI metros? Surely you don't go and waste perfectly good and healthy tanks (at however many shields apiece they cost, is it 100?) on suicide missions until you can brute-force your way past those nigh-invincible full-health infantry, do you?
Incidentally, what's the casualty rate of your troops? If you train a cavalry or a tank, do you expect it to be alive five turns from now? Ten turns? If and when multiplayer Civ III is possible, you'll be in a world of hurt trying to dislodge fortified rifles or infantry coupled with artillery on city defense without any artillery of your own. That the AI is incompetent on defense when rails are involved doesn't say anything about the inhereint superiority or inferiority of 1-movement units.
And about artillery specifically, think about it in long-term benefits. Your average throw-away cavalry (they really only have a small window of dominance...from Military Tradition, which isn't even a required Medieval tech, until Nationalism, which Scientific civs can get for free BEFORE Mil. Tradition). Anyhow, your average cavalry does how many points of damage before it kicks the bucket or retreats? 2? 3? A few may kill more than one unit before getting dispatched, but how many will get completely shut out before dying or being forced to retreat? And how many shields are you spending on these? Build artillery and that one piece (assuming you don't leave it unguarded and the AI captures it) is capable of doing dozens of hp of damage over the course of the game (more if you built it as a catapult at the beginning of the game and upgraded it over time) with no risk to itself. It doesn't move like cavalry or tanks, but it is invaluable for keeping attrition down to manageable levels. And if you are conquering a nation with rails in place, if you can attack it with tanks on the same turn, you can hit it with artillery, too. Of course, once you get Flight, then Bombers can be superior to land bombardment so long as the AIs don't have Flight, too, and shoot down your bombers.
Meh, you just play it your way and I'll just play it mine and the AI will be just as dead either way so we can both think we're correct.
