when auto-correct overcorrects

It was while going through a chunk of text for a teacher's guide that I'm writing that the Google Docs auto-correct function kicked in and told me not to write "hold on to" (3 words), but instead "hold onto" (2 words). I say this is incorrect. The root phrasal verb is "hold on," and you add the "to" when holding on to something. Note that, when you use the verb in the imperative, there is no "to": you don't shout "Hold onto!" right before a massive bus crash—you shout "Hold on!"

Dictionary.com seems to support me on this: it doesn't show "hold onto" as a possible phrasal verb. If you insist on including "to" as part of the phrasal verb, you should write the phrase as three words: "hold on to."

"Hold on to your butts."
—Samuel Jackson's ill-fated John Arnold, "Jurassic Park" (1993)

The online Cambridge dictionary disagrees with me, but fuck Cambridge. Note that, when you type "hold onto phrasal verb" as a search string into Google, the first few entries to come up will be for "hold on to." In fact, most of the entries on the first page of Google's search results show "hold on to." If you're a diehard descriptivist, then you must bow to predominant usage.