They used to do just that, though people could pay about $25-30 (in like, 2008 dollars! So that’s closer to $47 today) for ‘unlimited text plans’.

I know you mean charge just these bulk senders, but if they didn’t charge consumers a similar rate too, whoever wants to spam SMS can just set up farms of consumer SIMs and dump them onto the network that way. In fact, they already do this.