Folklore conjecture on the final size of random greedy triangle packing

Let $G(i)$ be the graph remaining after $i$ triangles have been removed in the random greedy triangle-packing process on the complete graph on $n$ vertices. Let $M$ be the stopping time when the process produces a triangle-free graph, and let $E(M)$ be its edge set. An event holds with high probability if its probability tends to $1$ as $n\to\infty$.

Folklore conjecture. With high probability,

$$|E(M)|=n^{3/2+o(1)}.$$

The conjecture reflects the belief that the final graph behaves like an Erdős–Rényi random graph with the same edge density. Estimating the final number of edges remains open; the paper notes that the best known upper bound is $n^{7/4+o(1)}$.