This is coming at the difference in the wrong way. Obviously よみました is one easily digestible unit of meaning, and in terms of Japanese that does use spaces (usually all kana writing aimed at young children), it would be a unit to itself. But よみ is also its own noun, and part of things that are more easily identifiable to us as compounds incorporating it (読み方, for example). So it also wouldn’t be strange or intuitive to think of the polite forms as stems plus add-ons, even before they really get that drilled in through grammar classes. And unlike English, “How many words are in this sentence?” just isn’t a thought likely to occur to native speakers in the first place, where the most digestible, least subjective or niche counting unit for writing by the time they’re cognizant enough of language to ever need such a thing is characters. Unless you’re doing grammar drilling, Japanese is pretty much always going to be counted in characters rather than anything else, whereas in English it’s words.
There are also issues with “word count” in Japanese for non grammar-focused speakers even without getting into things like the fact that verb “conjugations” are actually stem-based compounds, such as how to group particles and compounds where the break isn’t all that clear. (What do you do with three- and four-character jukugo phrases? Even as a native English speaker trained to look for “words” in foreign languages, there are some of those I wouldn’t really know how to classify.)
So while it’s true that you might need some grammar training to think of よみました as three words (but also not that much, because you’d see よみ as its own unit in plenty of other cases, and the polite form is already an extra step of conscientiousness on top of the plain forms kids speak in first), it’s also a bit of a projection from an English-native mindset to think that it would be automatic to consider it one.
English and Japanese are just … super-duper different, and the way native speakers think about their smallest practical units is one of the ways that’s true. For counting in Japanese, characters are easier. For parity in translation or for thinking about increasing your vocabulary, there are “phrases” (言葉, etc. - we tend to translate that as “words,” but it can include longer strings of language), but they won’t always line up with what an English speaker would look at and intuitively identify as single “words” either. Basically the two most useful, intuitive units of measurement in the language run either shorter or longer. Languages are just different, and they don’t always break up the same way.
But to the points above, I think the thing that best illustrates that difference is, if you ask a native Japanese speaker to count the number of words in a sentence, they’ll look at you like an alien and ask why you’re having them do this difficult and unintuitive grammar exercise instead of just counting characters. Conversely, if you asked an English-speaker to count the number of letters on their sentence, they’d ask why and if they couldn’t just count words (though at least both would be easy and objective in English; one would just be more tedious).
What is this all useful for? Not a ton really, in terms of how we learn Japanese. But maybe it’ll save someone from trying to bring up an idea like word-count with a native-speaker and expecting them to automatically be on board. (Again, it’s also just interesting.)
It’s however a paid platform, but offers 14 days of free trial 
I am delighted to have read your post! 