[peterjancelis]

Typically you are investing into getting new customers, so unless you can get CAC < first month payment[1], you will have a limited marketing budget hence a static number of new users.

[1] One way of achieving infinite marketing budget is to offer discounts for annual prepay, if e.g. you get 25% of customers to pay 10 months upfront (annual plan with 2 months free), you receive 25% * 10 + 75% * 1 = 3,25 monthly payments in month 1. If you get CAC below 3,25 ARPU then you have infinite marketing budget and that can indeed go geometric. But that's a big if, and even then at some point your marketing channels will dry up at some scale, while churn remains the same at scale as businesses keep dying or changing their mind.