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There is no one answer to this issue, whether supposedly proved by mathematics, logic or any other means.
There could only be a single answer if every sponsor had the exact same income and expenses and gave out the exact same share of their cut. Every site would need to retain at the same rate. Every site would need the same volume and quality of traffic, etc, etc.
As soon as any major variable changes, not least how hard a sponsor actually wants to sell the site that initially receives the traffic, the picture changes for the affiliate: regardless of the basis on which he/she is to be paid.
So we never get to compare like with like, thus even what we perceive as logic is likely flawed. For example, I go along with the generally popular view that TGP surfers are cheapskates, so I often point them at trials that offer me a generous one-time payment. It seems reasonable enough, but is it really the best option?
The bottom line is that I have no way to know. I can switch to a no-trial recurring sponsor. But if the results are different, let's say worse just for illustration, is that because this type of sponsor is a bad idea or because the particular sponsor I chose was a bad idea? Maybe my traffic sources changed. Maybe I just didn't get the sales pitch right. There is no way that I can reach any useful conclusions about the question of one-off payments vs. recurring income.
This topic has been around for years. If there were a convincing proof, it would have surfaced a long time ago.
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