(I also said it out loud for a bit before commenting lmao I love this "argument")

Counterargument:

You can say them, sure, but let's be slightly less theoretical about this, the word care has one vowel, but two noises. First you make a "k" sound for the c, then an "air" sound for the are. When we extending the noise, we extend the entire "air" rather than any individual noise that any of those letters make.

My argument is thus:

"Caaare," "Carrre," "Careee" and "Caaarrreee" all, when written, communicate to me that the "air" sound is being extended. None of these denote that the noise assigned to the letter in use is being extended despite their initial appearance to do so. Therefore, all three are valid spellings of the extended version of the word care.

My reasoning:

Definitions come from the way we use words, that's how Shakespeare got away with inventing so many words. He said or wrote them and then a bunch of people heard or read them and thought "yeah that collection of noises is acceptable to explain this feeling/object/concept/etc". Therefore, written words are only an indicator of meaning and not an actual reference point for information (if you're into computer science that phrasing will make sense, if not... Well I hope you're into computer science cause it's gonna take a me a while to figure out how to rephrase that in a way that makes more sense for what I'm trying to say). As a result, multiple spellings of the same spoken word may be valid because they're still capable of indicating the same meaning.