Every closed (not-necessarily symmetric) monoidal category is canonically self-enriched, right?

Question

Here it is stated that:

A closed symmetric monoidal category is canonically self-enriched.

This makes sense, but I don't see why it has to be symmetric. Every closed (not-necessarily symmetric) monoidal category is canonically self-enriched, right? If not, what goes wrong?

Answer 1

Ittay Weiss:

no need for symmetry at all.

Zhen Lin:

It is unusual to consider categories enriched in something other than a symmetric monoidal category in the first place – partly because a lot of the theory becomes awkward (e.g. opposite categories).