Bear in mind all the research and production bonuses that the AI gets on higher levels. If an emperor+ level AI used this strategy I don't think it would be possible to stop- you just wouldn't have time to get enough good units ready to stop them.Ok, where to start ...
Scenario 1.
There is a BIG flaw in your reasoning, that is to think that you can beeline to a enemy cap unharmed just like that. You can do that against the current AI, but that is just because you know they will most likely not attack you. Otherwise, would you take the risk to take your armies out of your territory to rush another player? Second, a competent oponent would know ages ago what you are doing, so in the moment you declared war they would be waitng for you. Third, in the moment you enter a enemy territory you are a sitting duck due to the extreme advantages the game rules give to active defense, so beelining to the enemy cap will surely put you in danger and you can only pull it out because the Civ IV is not that tactically gifted as that ( well, it beats the crap of a lot of humans ), but in games where the two warring parties are both tactically gifted you will see that the attacking part has huge issues to stay unharmed as soon as it enters enemy territory. Worse, the Civ III AI already had the bad habit of beelining for inner cities and that was extremely exploitable ( and exploited ). Go to the Civ III forums, search "kill zones" and see what I mean.... Fourth, if ALL the players in game did that ( remember, there are more than one AI and they do not cooperate to piss you off ) the sucess rate of that strat would be pretty low, most likely far lower than simply stay idle. Fifth, have you ever considered that a rush like that can fail by pure bad luck? And what after? You are left with a cripled empire with little pop and not much of techs against a enemy that is basically untouched ( because of your decision of going straight to cap ) ... IMHO that is a huge risk and should not be taken as lightly as that