Bitcoin certainly provides unique utility as an appreciating asset. It has given me a place to park the fruit of my labor that has appreciated in purchasing power far and above any other option. And processing more transactions per unit time allows a larger proportion of humanity to take advantage of this fact. This itself is a "significant and especially unique solution that it provides". Whether or not that is something you desire is irrelevant.
No it doesn't. You have said here that bitcoin is a good "alternative savings" but it does not follow and stand to reason that raising the tps will allow it to be this for more people.
One cannot park their wealth in anything without performing a transaction. And it is not really wealth, unless it can be converted back to products and services - which requires another transaction. Capping tps also caps the rate at which people can get in and out of this form of wealth (though that's a tautology). Yes, with capped tps there is a slider: a lot of people can get in and out once on one end, and very few people can get in & out at will at the other. But if unbounded participants can get in and out at will, then it starts becoming a money. The more liquid a store of wealth be, the more useful it is to those who control it. More utility: more value. More value: higher price. Higher price: better store of wealth. It's a virtuous circle.
When you mess with the underlying policies that effects the markets perception of it you introduce uncertainty. Uncertainty is what the markets don't want as a store of wealth ("alternative savings").
And BurtW has just told you that it had been an all-but-universal belief among Bitcoiners that scaling solutions would be forthcoming in some form or another. You seemed to accept this proposition. I certainly believe that to be true.
So if you are suddenly advancing the new proposition that Bitcoin should be artificially limited, it is you that is introducing uncertainty.
There is no economic literature that says that increasing the tps will increase the value.
If there is economic literature that says not increasing Bitcoin's tps will increase its value, kindly point me to it. Or if there is economic literature that says increasing Bitcoin's tps will not increase its value, kindly point me to that.
Lacking a mutually accepted reference, uncovering the truth will require either: reasoning it out; or running the experiment.
Reason tells me that more people getting more utility out of something would tend to increase its value (for any reasonable definition of value). So tear down that assertion.