You are correct that (at least as far as I know) there is indeed no explicit legal provision saying Tesla can’t just give SpaceX/Twitter/etc endless free services. However, Tesla is a Delaware corporation, and under Delaware corporate law (same as in most other jurisdictions), directors and officers have to take special care in conflict of interest situations, to avoid contravening their fiduciary duties (especially the duty of loyalty). The easiest way to make sure that duty is being appropriately discharged, is to ensure that those services are provided on commercial terms, which would normally involving paying for them. So while there may not be an explicit legal rule saying they have to do it this way, in practice their lawyers will be telling them this is their recommendation to minimise legal risk, and I have no doubt that they’ll listen to their lawyers and do what they say.

As well as the corporate law issues, the accounting and taxation implications of non-commercial transactions with other firms with which you have significant common ownership can be quite messy in many jurisdictions, which is another compelling argument for keeping those transactions on a commercial fee-for-service basis.