It's possible to have more than one reason for getting $75 billion from public markets. Paying off $20 billion of loans from people you don't want to owe money to (who, as far as I could tell, SpaceX borrowed money from to pay off people you really don't want to owe money to) and getting a really big number associated with your name are not mutually exclusive, and from Musk's previous actions (getting large compensation packages approved by conflicted boards) he obviously does want that number.

Even if only 5% of his NW is in cash, that'd be $50billion dollars in actual liquid cash. Even if it's 1% or less, he almost certainly has over $1bn in cash or practically liquid cash. That's already a dragon's hoard.