Yeah, well, you know, that’s just, like, your opinion, man. Since this is a new system, do you have any science to back it up?

Yes. Equal voting systems have been thoroughly researched through election method simulation of various voting systems. Approval voting in the first stage and a vote between the top two approved in the second stage is the highest-performing simple, unranked voting system. It also has a high propensity to elect the candidate that could beat all others one-on-one when such a candidate exists (the so-called Condorcet winner).
In an analysis of 51 different voting methods, including Range, Approval, Bucklin, IRV, Top 2 Plurality and many more, Approval with a Top Two outperformed all but two (Range and Range with a Top Two - also equal voting methods), and far outperformed the system we use today. It is by far the best system that uses a simple two-stage balloting system like the one we use today.