Nope, Bitcoin price does not fluctuate because of a big number of people trading back and forth between altcoins and BTC. Bitcoin is so volatile because it is a pretty new asset class and investors are not accustomed to. They don't know how to evaluate it so the price moves mainly due to speculation. Nowadays we see big companies like Tesla and Microstrategy hoarding BTC as a hedge against fiat and for capital appreciation. This trend could change the violent moves of BTC especially on the downside.
Another factor is the low liquidity in the markets. Institutions with deep pockets cannot get their hands on BTC yet, but only with very low amounts that do not impact their yearly performance significantly. That's why you see investment funds like Blackrock only "dabbling" with Bitcoin - because they don't want the market to get in a buying frenzy, at least not yet.
Let's not forget the law that plays the market of bitcoin or even in any kind of business in real life the "law of supply and demand". We are so delighted that we becoming a huge number of traders but on the other hand, the more that we increase in number especially the new joiner to our number are whales who can afford to avail as much bitcoin as they want, expect that the market value may vary accordingly. Bitcoin were made in a limited amount, and if the supply of bitcoin in the market has shortage it will definitely give an increase variation of market value and otherwise to the abundant supply of bitcoin.