Absolutely true, but ignorant stock traders making irrational trades only matters if company management pays attention to them. Musk will maintain complete control of SpaceX even after the IPO, so he can focus on long-term value rather than short-term ups and downs.
Of course, over time, if more shares are issued, this may change.
However, some projections I have seen suggest even the public raise won't be enough for the entire vision (which includes LEO data centers AND trips to the Moon and Mars). That means he will either have to find the revenue or eventually sell even more shares. It will only be at that point he will care about stock price.