A major reason the Senju and Uchiha were top 2 during the Warring States era wasn't only power but versatility and adaptability.

According to the guidebooks, the Senju Clan (Thousand Hands Clan) were named so because they didn't specialize in one talent but had many skills. These were Asura's followers and unless Asura was a really, really horny sonovabitch, there's no guarantee you were related to Asura instead of one of his followers. Given he had so many followers, it's likely they all had their own different talents and abilities. Thus, the Senjus were a jack-of-all-trades, but a master of them due to some members with lineage from Haguromo himself.

(By the way, the quote "jack of all trades, master of none", eventually got "oftentimes better than a master of one" added for good reason. Specialization is useful and all but overspecialization without anything to cover leaves you vulnerable. Rarely does war have some one-size-fits-all super weapon that makes everything else obsolete. Combined arms exist for good reason.)

The Uchiha Clan had massive Chakra as a genetic trait along with their Sharingan. Even ignoring the raw power MS gives, the regular Sharingan's ability to commit patent theft means they too have no hard-counter. Even countering all their Fire with Water just means they'll start copying your Water or they'll pull out another move they copied from a different battle. Their greater chakra means an Uchiha member might be able to outdo the original user too. And that's not counting the hypnosis, chakra detection, and other abilities. Kekkei Genkai abilities are rare enough (even demonized in some places) that hard-countering their copying is both hard, and just praying the Uchiha you fight don't already have a pre-copied solution.

(It begs the question if the Uchiha ever accumulated a collection, like a scroll or library, of very powerful and useful moves they stole from everyone else. Including extinct clans, making them the last known carriers of this knowledge. From what I can tell, especially given the Sharingan is rare among Uchiha pre-massacre, they don't have any or would've stopped maintaining them if they did. Might've been useful to have a chain of succession passing down copyright infringed materials, almost makes them look like digital pirates.)

Just think how hard it'd be to be both as capable as specialists without losing out on general abilities. A clan could be masters of Earth like Deidara but meet their own Sasuke Lightning user. They can have situational abilities that work better in conjunction, like a clan with ranged artillery-style blasts that collapse without bodyguards if they're ever rushed or ambushed in close range. A genjutsu clan that doesn't do much else. The Senju and Uchiha would have none of those downsides, either having a guy with the talent or the ability to copy and thus none of those vulnerabilities. Also, them fighting each other would've meant Uchiha spend more time copying Senju, and Senju developing new techniques would skew towards countering a growing list of Uchiha copyright thefts. It might've caused both to become stronger in a way. In the end, both are TOO good at being masters of all that no single clan could ever face either, even without factoring their enormous raw ower.

Also, the Hidden Village System made individual versatility (especially clan-level) still valuable but much less so because a ton of Clans (that may've been enemies) are now together. A theoretical all-close range clan that'd be seen as excessively overspecialized can now team up with others, including other hyper-specialists, to cover up their weaknesses. Thus the Senju Clan seemingly dissolved, and the Uchiha Clan became one of many clans (a bit a dominant clan) rather than having no peers or rivals with the Senjus not an entity anymore. It's nice being hypothetically better on a clan vs clan basis, but they're not better than everyone else combined, part of why the coup was destined to fail even if the Uchiha miraculously equaled everyone else's numbers. They've already created a system coordinating each other better than any single clan could ever, combined with powerful other bloodline-exclusive moves like the Hyugas, and just too many different types of fighters that copying two or ten wouldn't mean you won't be defeated by the next dozen. Nobody among the Uchiha there had the Madara level power to brute-force win a coup regardless of enemy to overcome this system of coordination. You'd need way more practically Kage level MS users than exist in canon to make the coup work.

In a way, it goes to show the success of Hashirama's ideals. It's not just realizing the Clans have the power and unionizing, it's creating a system where no single strongest clan could destroy the whole system from within. Which in the Warring States era, clearly no hired clan (excluding uber-exceptional members like Hashirama and Madara who could singlehandedly wipe whole villages anyway) could compete with not just the power but the management and organization of the Hidden Villages. Given the chaos and scale of the Great Shinobi Wars, the Hidden Villages are no less capable of big conflict than their previous era random clans, moreso given Hidden Villages vs other Hidden Villages rather than one-off clans. For better or worse, Hashirama also created a more efficient management style to make war and individual armies stronger. At least child mortality rates are down.

(BTW, pre-Hidden Village Clan alliances do seem to exist. Ino–Shika–Chō is in its 17th generation during Boruto, which means 16th is the Naruto cast, and their parents is 15th. Even if a number of past generations were teen pregnancies, they clearly have enough generations that they'd be active during the Warring States era. But not only is that paying for 3 lesser known clans than a single famous clan, this doesn't sound like a super common thing. And the synergy of Ino–Shika–Chō doesn't mean they're as versatile as the Senju Clan's many members or Uchiha copying. I doubt fully trusted clan team-ups were the norm in the Warring States Era anyway. Yesterday's ally could be tomorrow's enemy.)

TL DR: You can't hard-counter Senjus or Uchihas so even without their raw strength, they'd still be dominant through versatility.