Raising the difficulty in a strategy game rarely makes the opponent think better. It gives the opponent more, and understanding why explains a great deal about the genre.
Strategic reasoning is computationally enormous
A strategy game presents a very large number of possible actions each turn, and evaluating them requires considering how an opponent would respond to each.
The number of positions grows so quickly that exhaustive analysis is impossible, and unlike a board game there is no compact way to evaluate a partial state.
Systems that play such games well exist, but they require resources far beyond what can run alongside a game on a player's machine.
Scripted behaviour is what actually ships
Most opponents follow authored routines: build orders, thresholds that trigger attacks, and rules about which units to produce given what has been seen.
These work well against inexperienced players and poorly against experienced ones, because a fixed routine can be learned and then exploited indefinitely.
Making the routine more sophisticated helps somewhat, but each addition is written by hand and each interacts with the others, so complexity grows faster than competence.
Resource bonuses are cheap and effective
Giving the opponent faster production, cheaper units or additional starting assets raises the challenge without requiring any improvement in decision quality.
It is also easy to tune, since a single multiplier can be adjusted to produce a smooth range of difficulty settings across the whole game.
The cost is that the player is now solving a different problem, defeating a stronger economy rather than a smarter opponent, which changes what the game teaches.
Visibility bonuses are the more contentious kind
Some designs let the opponent see through fog of war or know the player's composition, which removes the scouting decisions that give the genre much of its depth.
The behaviour is often noticeable, since the opponent responds to a strategy before any evidence of it could have reached them.
Players describe this as cheating rather than difficulty, and many modern games avoid it specifically because the loss of trust outweighs the challenge gained.
Personality is a better use of the effort
Rather than pursuing optimal play, many designers give opponents distinct tendencies: one that expands aggressively, one that turtles, one that raids constantly.
Distinct behaviour is memorable and forces the player to adapt, which produces the variety that raw difficulty scaling never delivers.
It also fails more gracefully, because an opponent with a recognisable character remains interesting to beat even after the player has learned exactly how to beat it.