The other factor is that I don't think SpaceX see software as a differentiator. They have talented software engineers, sure, but a lot will be a very different type of software engineering to the typical FAANG sort, lots more real-time and embedded software. I believe their main piece of non-real-time/embedded software is their inventory/work management application which is all on the Microsoft stack. My gut feeling, could be wrong, is that your average .NET dev makes less than your average dev at a FAANG company. The market may just not need the higher salaries.
I know a number of people working in engineering in SpaceX (as in, designing the rockets or modules), and most of them are making between 50k and 90k, despite having PhDs or years of experience in aerospace engineering. To put the salary in perspective, a few of these people took a pay cut when they left JPL to work for SpaceX.
They work at SpaceX because they find the work exciting and rewarding, but if you're in it for the money you'll have to work at one of their competitors.