Bitcoin will never be stable. Its price comes from the free market. It wasn't made for stability. It was made for value growth, self-banking/secure/decentralized/censorship-resistance, and for transacting. Stability in price was never part of the deal.
It
can be stable; at least stable enough to be viable to be used as a day-to-day currency that's not going to move +-10% in a day. It's just that it's going to take a while. Bitcoin can come to the point that it will be sufficiently stable, but at the same time still be in an upward trajectory in the long term.
It can be
more stable. It can never be stable. Volatility will go down as the market matures which just means the market cap gets larger and therefore harder to move around a lot. Volatility has continually gone down over the long term as Bitcoin has gotten bigger and bigger and that will continue. But yeah like you say its long term upward price trajectory will continue even as short term volatility falls over the years, so I don't see that creating an atmosphere where suddenly people are gonna be like hey lets all spend our bitcoin on a day to day basis rather than holding. Holding will still generate value so it will always be preferable to spending.
Spending Bitcoin has more to do with when each person is happy with what they've made and spending some of that on something, and has less to do with volatility. Knowing that Bitcoin could be 2% higher or lower tomorrow compared to 10% higher or lower tomorrow doesn't make a difference in spending - you still get the purchasing power of whatever the price is at the moment you spend it. You're only going to make the decision to spend if you're happy about how much value Bitcoin has already created for you and you feel comfortable spending some of that value, volatility doesn't come into play in that decision.
Short term volatility is more of an impediment to getting PAID in Bitcoin. You don't want your paycheck in a month to be worth 20% less than what it was when you got it. Make a purchase is instantaneous so volatility doesn't play a role in it, but you don't spend your paycheck the moment you get it so that is where volatility affects things. What we could see as Bitcoin matures and becomes more stable is more people taking their paychecks in Bitcoin. But the hurdles to spending are not volatility but tax rules, merchant acceptance, and tx fees. If Bitcoin merchant acceptance becomes ubiquitous, if LN became usage became ubiquitous so tx fees were not an issue, and if spending Bitcoin didn't incur capital gains taxes then Bitcoin would be ready to be a daily spendable currency, but only by people who were already happy with how much value they'd already generated through Bitcoin.