There’s a rock-paper-scissor game design in Total War, and in video games in general. They tend to distort things quite a bit in order to make it more interesting from a gameplay perspective. In general, no, it is not realistic.
Like, spearmen are kinda even with swordsmen in a pitched battle, and you can run either down with cavalry if they're tired or disorganized, but you usually can't leave cavalry committed. There are only a couple of minor damage bonuses for balancing, not like AoE where you have the "anti-cavalry spearmen" etc.
Total War definitely has an element of rock-paper-scissors design (particularly between cavalry/archer/spears), pretty sure its even referred to explicitly as such in some of the official strategy guides for titles in the series.
(It's also not an RTS franchise, its RTT + TBS.)
> There are only a couple of bonuses like spears vs cavalry, and the rest is mostly situational.
That some of the advantages are properties of interactions off basic traits and not explicit class v. class bonuses doesn't make it not a rock-paper-scissors design.
Spearmen purpose was to buy you time and for other units to tire out, before you'd bring in your swords :D
And every community had their own...
WH 3 basically solved this issue by making MP battles be capture the points style - genuinely, it freed us from having to make house rules.