Mate, I don't really understand that you said the price won't be very volatile when the market cap grows high. Does the high market cap really decrease the volatility of Bitcoin? 
Well, I'm not an economic expert but I guess when Bitcoin's market cap grows to 100's of trillions in future then it's volatility will reduce. The more market cap might help to reduce the volatility of Bitcoin and their might not be similar level of dips when market grows by a huge level. Let's say if somehow Bitcoin grows to 100 Trillion market cap within 5-10 years then that might help to reduce the volatility of it. When market cap gets higher so does the liquidity and some asset with high liquidity might be less volatile than an asset with low liquidity.
This is easy to see just by looking at bitcoin's year-over-year growth. Do we still see bitcoin giving 1000%, 100000% returns if someone invests in bitcoin these days? Did we see Bitcoin go 10x, 100x in the latest bull run? It is almost certain that those things are in the past and we will never have the chance to witness those wonders again. That alone shows that as bitcoin matures and its capitalization increases, its returns will diminish over time. But that's not necessarily a bad thing because the larger the capitalization, the more liquid and safer it is.
By the way, your assumption is too exaggerated, bitcoin's capitalization will never reach that level. $100 trillion is the market capitalization of the entire world's stock market today, and that's not an easy number to achieve. I just hope in 30 years bitcoin's capitalization can be equal to gold and this will be a huge success.