Why Range vs Range and not Hand vs Range

In solver both players know range of other player. If you put only one hand in your range, the other player will know exact hand, so you get meaningless result.

Not a solver nerd, but enjoyed considering your question and offer some thoughts.

Knowing how your range behaves should help you determine how your specific hand will do. Solvers compute how each individual hand combo in a range performs against villain’s range. With this general knowledge and the related frequencies & sizings, a player can consider what to do at the top, or bottom of his range.

Incomplete information is poker. We are guessing most of the time. But the info gathered is where we hang our hat. We set up a different range for a nit and a station, but they could deviate. We narrow down as we go. But we must also consider our image, what does villain think of us.

Knowing how your range and villain’s range interacts with the board is next. If you miss everything, but the board hits your range, it could be a chance to bluff. Though it may be possible, I don’t think computing hand vs range would be as helpful as you think.

Yeah it's to do with how GTO/nash calculates. GTO will optimise to whatever parameters you feed it. So if you only give it one hand, then your opponent's range will calculate around that sole input (something an opponent is never doing, ofc, as they can't see our hand).. thus producing a useless strategic output.

The solver can't figure out how to optimize villain's strategy without making some assumptions about what hero is representing. If you have no range, how does villain know what's a good strategy? If villain can't figure out a strategy, then there's no way to figure out the best way to play your hand.

If you plug in just your hand, the solver will treat it as if your hand is face up.
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Let's try an analogy. Imagine I give you this nonsensical hand history:

"So there I was on the river, I go for a huge bluff and get snap called by top pair. What do you think, bad luck or bad play?"

You say: What was your table image?
"It doesn't matter, I had a bluff", I say incredulously.

What was the action leading up to the river?
"Who cares, I already told you I had a bluff..."

What were you representing?"
"What does it matter?! I know what hand I had, who cares what I could have had!"

Well, it matters because villain's decision to call or fold is contingent on what you're representing.
Maybe you were playing any two and spewing stacks in a drunken rage all night. Maybe this is the first time you've bet the river with anything less than two pair in 5 years. I have no way of telling you whether or not your bluff was good without the context of your range.

Even absent villains reaction to your strategy, your own optimal strategy can change depending on your range in a particular spot. Just as a simple example, I have some hand that has missed the board. Should I bluff the river? The answer might well depend on your range of hands that reaches the river in this spot. Are there a lot of natural bluffs in your range, one’s better than your current hand? If so, then probably you shouldn’t bluff. Is my range value heavy and lacking in bluff candidates? Then probably yes you should bluff. Same hand, different answer depending on your range.

The theory part of this seems to have been largely covered, but the part of your post I've quoted appears to be you hinting at a more exploitative mindset, at trying to get more chips than your range would get on average for a given board.

Other hands definitely are changing your strategy and consider spots where you range check in theory - you will likely still have hands worth a ton of chips that would want to shovel money in, if it weren't for all the other hands you have bringing it down (e.g SB vs BB single raised pot 654 rainbow board, you as preflop aggressor will still have 87 in range here).

As others have mentioned, this might not go so well. Consider an OMC type who raises AA preflop and limp calls or limp folds everything else. If the other players at the table are unaware of what the OMC is doing, AA's EV isn't going to change, but if people do realise and adjust, AA's EV plummets as people range fold pre. As other people have mentioned, the solver would follow suit in folding pre since you'd have to plug in only AA was being raised.

Again as others have mentioned, solver will optimise around that hand only being the one in range. You can nodelock to get around this though, as in reality, it's quite difficult for people to figure out exactly what you're doing without a significant data sample (provided you're not extremely obvious about it), so most players at your tables are unaware of your strategy and won't adjust properly to you deviating.

So by all means, have 87 be the only hand you're not range checking with on a 654 board, if your opponents are not going to notice (or more specifically adapt) you'll likely get more chips than the alternative, without suffering the backlash of never having the nuts in range when you check that board.