One-time fees are not very sustainable. Unless the model included essentially building an endowment the first ten years and then funding the business off of interest.
One-time fees are a perfectly fine model for a business, even if it is unfashionable currently.
Twitter, Facebook, and Google have used ads to collect revenue from their users in the past. SaaS apps and services today use recurring subscriptions, which is nice because it lets you match up your inflows to your outflows. Old desktop software, which had high recurring costs too, used single payments (although they also charged for updates). Modern desktop software tends to use subscription fees.
Companies need to make their revenue models match what customers expect in order to get payment. That means that you should be selling your SaaS as a subscription or a metered API even if you (hypothetically) do not have recurring costs. It also means that Twitter might have to stay with a $0/month fee and collect its revenue in the form of ads and "direct payments for services."
For Twitter, "influencers" might pay as much as $1000 for a "verified influencer" label on their profile despite that many of them are upset at $20/month, particularly if you make it annoying for them (so they feel that they are actually spending their money on getting "verified" and the verification will be hard to fake). Maybe you can get $100/year as a "renewal fee" on those labels, too. If you offered the rest of us a $50 "not a bot" green checkmark that takes a few custom photos and an ID, you will probably get plenty of those too.
It's all psychology. Fixed fees and recurring fees can have the same NPV. The game is maximizing that NPV.
> and there will always be new people using popular products.
If you succeed in being the go-to platform for every new generation you might be able to coast on that. But the last 20 years have shown that each generation gets its own new social network.
> Unless the model included essentially building an endowment the first ten years and then funding the business off interest.
Ten dollars is surely much greater than the server costs for a single user for a month, or a year. That one-time cost may well be designed to be an endowment of sorts. Plus the avatar changing fees are probably, on average, not one-time fees.