"Patrulo" would also work.

"Ino" and "ulo" are practically redundant, which makes it (I think) the easiest way to sneak in a masculating affix.

Like some other languages, one of the two is both specifically male in some contexts, and generic in others (which is why vir- exists, to clear up confusion in otherwise-generic contexts). English even retains some irregular words of this sort, such as dog vs. bitch, where dog is male in contexts where gender matters, but bitch is female in all contexts (at least when it comes to dogs).

Only one gender can get the shorter prefix, and there are only so many vowels (many people say that Esperanto already has too many vowels). Real surviving cultures aren't so petty that they'd make all their words longer by two characters for the sake of "fairness".

As for -in* being two extra characters for explicit-feminine, it's just something you trade for regular conjugation with such restricted phonotactics.

Now, you could make the argument to ditch grammatical gender altogether, and I'd probably be on board with that. In most cases it does not shorten or clarify sentences.

"vir-" is a preëxisting masculating prefix. I would read patrulo as "A fatherly person", rather than a parent, as "-ul-" turns an adjective into a person embodying that adjective.

(ge- is the neuterizing prefix, but in my extremely limited dabbling, it's mostly seen in plurals: gepatroj for parents, but for a single parent, one generally says patro for father and patrino for mother.)

Wouldn't adding an extra syllable to a large subset of words indeed be a language problem?

That‘s not sexism though.

Male-by-default isn't sexism? What do you mean by sexism?