This has a lot of possible answers. One wants to say, as many answers as there are research proposals.
In mathematics, some things matter just for the pure beauty of it. The same may be true in other fields. Probably true in the arts as well.
In CS one can often search for improvements on current best practice - faster, more secure, smaller, simpler.
Some problems matter because the search for answers has been long and unfruitful. Some things in physics are like that.
Some things matter because they provide synergy between existing ideas thought to be distinct. Drug research, pedagogical research.
Some things are useful. And, as you say, one can hope that other things become useful in the future. Very fresh pure math may have few current uses. But potentially future uses.
Think about why you want to do the research. Think about how it will complete something from the past. Think about how it might foreshadow the future.
I'm sure you can come up with something. And it need not matter to everyone. Sometimes it will only "matter" to a small group of specialists. Math can be like that too.
And they aren't mutually exclusive. Quite a few of these were manifest in my own doctoral research.