After a while, the price would "stick". People wouldn't put fortunes in it, they would only acquire what they need to use as a currency. They wouldn't be watching coinmarketcap to see what goes up and what goes down. It would just be a real currency.
This is just pure speculation.
In fact, almost all altcoins follow the exact opposite pattern to what you've described. They launch, and price rallies massively, then they slowly tail off down to effectively 0. There are exceptions, but most follow this pattern.
Of course, because no alt coin ever had a demand driven by
a currency need (same fool). Every crypto currency that launches, bitcoin included, is launched as
a greater-fool token, which booms and busts. Do you know many people buying an alt coin because they expect it to be stable in value ?
In fact the ONLY alt coin that has NO expectations of rise, and is working more or less as I describe, is Tether. You cannot really redeem Tether for dollars. So whether it is backed or not doesn't mean shit. People buy tether as a currency. Nobody speculates on tether. So the market cap of tether represents a demand of currency, that is "transporter of value". Slowly, the price sticks: one tether is $1. Now, it is visibly true that tether can shrink somewhat its offer, and as far as I understand, this has been done very lightly, only twice. When you look at the momentous rise of tether's market cap, and the stability of its price, essentially through emission, you get an idea.
Your argument actually supports what I'm saying: almost all altcoins that don't have price control, are speculative greater fool assets, MAINLY acquired with the hope of a rise (and we know what that means: bubble - burst - bubble - burst ....). Almost none of them are acquired to keep a steady value. So they, indeed, bubble. And bitcoin bubbles too, it is not different.
A coin where there is no hope for a large rise, and with a predictable price maximum, is only bought when it is useful. And when it is useful, there's no bubble-burst. There is no bread bubble. There is no butter bubble.