Related yes, but causality only runs in one direction and it is toward mining not away from it. Empirical evidence (which is hiding on this forum somewhere unless the author deleted it, which I doubt, but I can't find it) is that mining is driven by price, not the other way around. That is to say, you get the mining demanded by those who compete to hold the coin by driving up the price; you don't get the price driven higher by more mining. This also follows logically from the one-way function of static output difficulty retargeting, which confuses intuition because there are few if any non-virtual markets with similar structure. You could probably get a different result with different retargeting though.

This doesn't answer the question of what does create and drive demand for the coin, just what doesn't (mining).

Somewhat tangential, but when I commented on crypto-to-crypto exchange being frictionless the context was not multiple competing currencies,  it was people wanting the coin buying it instead of mining. To replace LTC you need only address the market of crypto owners (95%+ BTC), who can and will simply buy it, leaving the necessary job of mining to the experts and most efficient operators. Specialization reigns.

Beyond the scale of replacing LTC the situation changes certainly. I didn't address that at all.