How does "new money"'s perception of the coin change if the inflation period is long? I mean, what benefits are there in the long inflation period for investors? How is growing economy of the coin dependent on the length of the inflation period?
Nobody loves inflation, but few people regard it as a horrendous evil to be avoided at any cost. Normal people do not expect that a hoard of cash will keep its value, much less grow more valuable, by itself, over time. And, for the good of the economy, they shouldn't "invest" in cash or other "dead" assets: they should use their intelligence to choose productive enterprises, and invest in them.
Cryptocurrencies were meant to be means of payment; their repurposing as long-term investment has always been criticized by economists.