Because everything anyone has ever told me about Elizabeth leads me to believe that her chief military advantage involves teching ahead of her rivals. I'm sure she does a great job of doing that one thing in particular, but I'm not going to call her versatile if that's the only ace up her sleeve.
Maybe not versatile in approaching the military, but the question posed by the OP was in regards to versatility in overall victory conditions. Not versatility within one type of victory.
Secondly, that is not her only ace up her puffy sleeves.
Ace of Hearts: Techs to modern units and uses them to defeat larger less advanced armies. I chose hearts for thios ace because it represents the philosophical side that gets the bulbed techs.
Ace of Clubs: Redcoats. If i need to explain Redcoats to anyone they should go play Age of Empires or one of the other mindless clones for theose with quick thumbs and slow minds.(Can you guess who hates Microcrap?). Chose clubs for the violent nature of a club.
Ace of Diamonds: The UB Stock Exchange provides 15% got gold, more gold means supporting more troops and handling more conquered cities.
There are your aces, I have addressed all three aspects that define a leader. The traits, UB for their civ and the UU for the civ. There are no other differences between leaders than traits, UU and UB. I have shown where she has something of an advantage in all three....now combine all those advantages and you have a mean bitter lady that is best to not be trifled with.
HC is a great leader but in an isolated start his UU is useless unless you think you need an edge against barbarians. And so is the Ub. who do you need to win a culture fight on the border with? By the time you get to the AI lands they have a lot of ancient culture built up.
And even on a map with other AI on the starting landmass a Quecha rush is situational. I wouldn't try it vs a protective leader, or even one with a capital city on a hill. Can you get enough Quecha built before the AI has BW and copper hooked up? The AI target needs to be very close by. One whipped axeman fortified in a city can eat a lot of quecha. Will you have enough left over to take the archers as well?
Cheap forges are nice but cheap universities are better. Forges usually go in cities with decent production to begin with where universities go in production poor/commerce rich cities. And 15% extra commerce on top of the finacial boost is big...really big. Usually good for a notch on the tech slider. And when you drop the slider to 0% for gold to upgrade (remember you get the miltary techs sooner) you get a sizable boost in gold for up grading to, oh let's just say. REDCOATS.