I would like to challenge the framing of the primary thrust of this question: the notion that "flat" design is a good idea.
Game design is really not that different from plot structure in narrative entertainment (movies, TV shows, books, etc). In a plot, things start off simple. Then, a complication occurs. Then a couple more. More conflict is added. This builds and builds until finally you reach a climactic encounter, followed by the resolution.
How fast such dynamics in plot structure change over the course of a story represents the "pacing" of a story. In a fast-paced story, things change quickly and dynamically, with new complications happening sometimes faster than you can react to. In a slower-paced story, complications are added more deliberately.
But in pretty much every work of fiction, the plot gets more complex with time, not less. Or at the very least, the complexity is frequently changing. New characters are added, other characters are removed. New villains crop up, or new plans are revealed. Etc.
And this works in game design as well. At the start of a game, you have a few tools to tackle challenges. Over the course of the game, you either gain new abilities, or you learn how to use your existing toolset to deal with greater and more complex challenges. And so forth and so on, until it builds to a climactic encounter that (presumably) tests a great many of your acquired/understood skills.
A game of StarCraft works much the same way. You start off small and slow. Over the course of the game, you gain new abilities and powers, and you choose to employ them in a variety of ways. You have skirmishes, then major fights for territory. You're forced to expand, lest you fall behind. At some point, you have a decisive encounter which decides who wins.
This is how it works, and this is a good thing. Having a game play out in a well-paced way allows players to follow through on that narrative progression. A slow build over the course of play, gradually testing their abilities until at last there is the climax.
StarCraft is fast paced, such that it's essentially impossible to feel comfortable about anything. At all times, there is something more you could be doing, or something you ought to be worried about. That "drinking from a firehose" effect is exactly how SC is supposed to work, and that is due to the game's pacing.
Even board games like Chess and Go have pacing. People often talk about phases of the game, because as the game progresses, it becomes a very different game. And that's a good thing; that's one of the reasons why these games have been around for as long as they have.
Making a game "flat" would be analogous to a plot that doesn't change. Where it's the same plot from the beginning of the movie/book/TV show to the end. There's no build-up, no increasing complexity, no climactic encounter. It's just two people looking at each other and maybe swinging a sword every now and then.
It would get incredibly boring. You have to switch things up, change the dynamics, move from one idea to the next. Your plot/game design must advance or it is stagnant. And advancement means adding complexity, changing and reinterpreting the dynamics of play.
Change is just as necessary for game design as it is for plot structure. To throw that away, to discard pacing as a game design tool, is to effectively throw away what people are interested in.
There are such games in other genres, such as fighting games where, ignoring the power-up bar, gameplay does not change much at all over time.
This seems to show that what you're not interested in is not "flat" play, but something else. Fighting games very much do change over time. They have dynamic evolution of play. Positioning matters in a fighting game. If you're in the corner, you lose the ability to control distance effectively. If you're knocked down, you have to deal with all kinds of stuff your opponent can do to you.
The gameplay of fighting games very much does change. What fighting games do not have that RTS's do have is this: permanence.
In an RTS game, you win by denying your opponent the ability to play the game anymore. And I don't mean in the sense that the game declares you the winner. I mean that your every minor victory denies something to your opponent. You destroy some of their units, so the time spent building them is lost. You destroy a base of theirs, so the time and resources spent on them is lost.
You may be able to rebuild an army you lost, but it won't be that particular army that you just lost. Much like Chess; you may be able to promote a pawn, but they still lost whatever thing they replaced. In an RTS, you are fighting for your fundamental ability to affect the game.
In a fighting game, you're fighting for points. A round ends when one side scores enough "points" to defeat the other.
Because of this, every advantage in fighting games is entirely transitory, of the moment. Vortex setups on wake up can still be beaten if you guess right. Being pinned in the corner is a situation you can fight out of. And once you do get out of the bad positioning, you're back to essentially a neutral game (mechanically speaking. Mentally speaking, you're in a very different place).
Worst case, you lose a round. Yet another "point" you've lost, but it's just another point. You restart the next round back at neutral positions, with (more or less) the same situation you started the last round in.
Even damaging your opponent is a temporary victory. They go into hitstun and move backwards, giving you the potential to combo them. But after that, they're either still standing or on their back, a state that they'll recover from quickly enough.
In a fighting game, advantages are temporary. That's what gives you the sense that their gameplay is "flat", that it doesn't change. It does change; it simply resets quickly.
But the reason for this difference is that RTS games are primarily and mechanically about growth. You build stuff, whether its units, buildings, or both. You move out onto the map and gain territory. And so forth. You lose the game when your opponent destroys your ability to grow anymore (more or less).
If you want to make an RTS more like a fighting game, you have to make it less like... an RTS. You have to take away growth. You have to be able to make advantages transitory. You have to make victory work based on a more abstract system, rather than some battlefield condition of still being able to participate.