It's indeed impossible for the bitcoin price to remain in one place for 1 full circle. It's not even that possible. Under a year. The price will definitely be moving up and down, but let's assume the impossible happens and that's the case here, then bitcoin will mostly be used by those who want security over the transaction and protection over their holding, being treated as a reliable payment option among parties since they won't have to bother about price change.

1.Who says that Bitcoin's biggest strength is the price? Can you mention anyone in particular?
2.No price can remain stable and rock solid for 10 years. A market price is determined by supply and demand and those levels of supply and demand are constantly changing. Having higher price elasticity can be good for an asset, because it attracts traders and investors.
A market price is tied to value. If an asset or resource has an extremely low price, this means that the asset or resources has very low value. Bitcoin has a relatively high price, which means it has high value as well. Bitcoin's value is built upon decentralization and trust.

If the price isn't fluctuate,  I will say that bitcoin can lose its main attraction. But no matter how much we tell them decentralization is why they use Bitcoin, most people are simply a bunch of people hoping to make profit. If it is not moving for 10 years, investors might be completely distracted from it but those who want to control their funds will definitely utilize it, I mean for decentralization. I believe the biggest impact will be on the mining industry. If the price doesn't rise and the block reward goes down, miners will not have any reason to continue to maintain the network at this massive expense. Also  if it is an inflationary market, the stability of the price of an asset would mean that at the end of the day, the value of the asset will decrease and it is very hard to keep the network afloat solely with technical emotions.

Suppose we leave Bitcoins price aside meaning we consider it stable. Since everything has a certain value let’s assume that the value of one Bitcoin is one dollar so the value of 21 million Bitcoins is $21m (I said dollars just to explain).

Suppose even if the price of the dollar goes down the value of Bitcoin will remain exactly the same. Since Bitcoin has a limited supply people will want to hold these 21 million dollars because there is no other currency in the world more secure and trustworthy than Bitcoin and the value of the asset will not decrease. Even if the value of every currency in the whole world goes down Bitcoin’s value will remain exactly the same.

So whenever scarcity is created people will buy it for more than its stable price and in hand to hand transactions sellers will also sell it at a higher price. That means Bitcoin’s biggest strength is never its price.