The fleets were capable of doing as the lore states they did. The ships and technology has come a long way as the years have passed, however, and what was flown then is not necessarily what is flown now, even if some of the ship designs are similar. Stuff gets upgraded and retrofitted over time. Note, for example, how Amarr armageddons posted at stargates still use lasers, while new ones built today are designed as neut/missile/drone boats.
What the current state is, however, is not an organic stalemate. In the current time, equipment is mandated to be shared between every faction. It is a CONCORD regulation to prevent any single empire from becoming more powerful than another by basically destroying any notion of an arms race. This explains why ships between the factions are rather balanced between each other in the EVE of today. The stalemate is one that is forced by an external power.
But you can still see the lore influence on tech trees. Amarr’s choice of tracking disruptors and neutralizers, ewar that works best against Amarr ships, shows that they are most prepared for fighting other Amarr, due to having no real external military threat until relatively recently in their history (the Khanid Kingdom, which outright rebelled, uses cruors even. It’s always been my opinion that blood raider tech was actually designed first by the Kingdom to use against the Amarr Empire during their rebellion, and was only later sold to the blood raiders). Minmatar ships meanwhile are designed to be speedy and have limited reliance on capacitor, negating the effects of neuts and reducing the power of lasers due to their poor tracking. Minmatar missile ships negate Amarr tracking disruptors. In Gallente/Caldari tech, the shared use of hybrids shows the common roots, and the ewar again shows how the tactics developed. Caldari use ecm and long range missiles and railguns (as well as fighter deployments, in lore), which shows an intent to negate the superior numbers of gallente from effectively counterattacking. These tactics then prompted Gallente development of drones and damps, enabling the ability to attack even under ECM (and to fend off fighter craft) and to force missile/railgun ships to engage at closer ranges.
And then comes tech II ships, which have resistance profiles designed to counter the enemy faction. While CONCORD rules require the sharing of technology, even in this current equalized setting it’s clear that the factions are still attempting to develop their technology in ways that counter what the enemy can do.
As for the ability for capsuleers to customize and mold their ships so freely? I consider this to be one of the big reasons why capsuleers have become such a force in the cluster. Certainly the superior piloting ability and cloning is useful, but the reduced crew requirements enable ships to be built with modularity in mind. Capsuleers are absolutely supposed to be more capable than any traditional fleet, because capsuleers are the next step in the evolution of warfare. Compare it to the real world’s drifting away from large, pitched battles between armies to small scale, high tech unconventional warfare. Capsuleers still have large battles between massive fleets, but modern technology makes it essential that you can adapt on the fly to changing situations. The empires have the capability to a point, and have their own capsuleers, but it’s becoming very clear that traditional tactics and fleet compositions just don’t work in the modern era. The empires outright admit this in the force auxiliary descriptions. Traditional bridge captains and static, unmodular ship designs are getting left behind in favor of newer or retrofitted designs piloted by capsuleers.
As for the ship factions? I think this has more to do with the lack of a real ongoing war than anything else. I expect that if a real war between the empires broke out, they’d start developing their own ships that make use of technologies from other factions. There’s just no real need for it right now. That’s the big difference between independent capsuleers and the empires. Capsuleers make use of a hodge podge of tech from the various factions, but they don’t make their own. The empires however are able to do research and development and create their own new designs. If a real war broke out, you’d see local factional ships designed to use whatever tech was most useful for fighting the enemy, instead of just grabbing another faction’s ship.