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. Having bitcoin as a store of wealth and using it to transact are not the same thing.
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").
There is no economic literature that says that increasing the tps will increase the value. It's not founded. It is a tacitly held assumption.