Why is an 'e' necessary to make "potato" plural?

Spelling in English is sometimes based on pronunciation and sometimes there are arcane rules.

In the case of potato (and mosquito, and buffalo, etc.) the rule is to use -es when the o sound is a long o that follows a consonant. This is so that you don't see the word potatos and think POTAYTOSS. Another arcane rule here is that if the O follows a vowel, you don't use the extra e, like radio/radios.

There are, of course, exceptions. Magneto plural is "magnetos".

I doubt it's knowable "why".

English orthography - how a word and its spelling are related - doesn't start with a rule and work from that. Any rules are observed ones based on how historical spellings played out over centuries of uncoordinated development. Sometimes that results in clear patterns you could call "rules", but there are often (if not usually) exceptions, and even completely inexplicable one-offs.

For whatever reason, "potatoes" kicked off right from the start as the vastly dominant spelling, especially from the mid-1750s, when the potato's popularity really caught on.

See Google Books Ngram Viewer for print stats over time for "potatos" vs. "potatoes" https://books.google.com/ngrams/graph?content=pota...

I guess I never had to write the word before - it just looked extraneous and wrong.