Latała's conjecture on the norm of structured random matrices

Let $X=(X_{ij})_{1\leq i,j\leq n}$ be the random matrix in the setting of the section, with independent centered Gaussian entries as specified there, and let $\|X\|$ denote its operator norm. Latała's conjecture.

$$\mathbf{E}\|X\|\asymp \mathbf{E}\max_{i\leq n}\sqrt{\sum_{j=1}^n X_{ij}^2}.$$

This was proposed by Rafał Latała, inspired by results of Seginer for matrices with identically distributed independent entries. The source presents it as a competing conjecture to the preceding bound, with no resolution supplied.