Example: Up to 3000 messages/month bill this credit card (my credit card in my saas business), after that a different one (my clients)

Trying to fuigure that one out - are your businesses really that simple? Because I am also adding 5-6 or more third party services for most clients - and the question who pays is a major one if you deal with a lot of businesses. Small ones may not understand that, large ones mean paperwor kfor every case, which is awful - best seems to be in BOTH cases to write an invoice to the client.

Yeah I wonder as well with more third party apps and api calls, invoicing must be a nightmare

Internally not so much - but imagine you are a freelacer or a not tech affine company - you suddenly are expected to manage half a dozen service accounts and any mistake is a nightmare. On top, you better use virtual cards, as any change on the card otherwise is a nighmare in account changes. I can tell you a lot of companies do not want to deal with this - WAY easier to pay one agency once per month. And as I said - the moment you go larger company, the paperwork would kill them. This is likely a new approval process for every small provider.