Write an English T. If you do the horizontal stroke first it's really easy to ensure the vertical stroke starts exactly on the horizontal stroke. The other way round is harder. This matters in Chinese because there are lots of similar characters and sometimes the only difference is whether lines meet or cross. Even when there are other differences, getting it right helps the reader.

(subjective experience) When writing fast the result will be easier to read if you wrote with the correct order. Writing a character on your phone with the correct stroke order will increase the chances of finding the character you want.

Stroke order is less important than you might think, and than what most learning materials make it out to be. But an idea on the general order is crucial to writing fast, and also, quick writing that does not follow either (1) the standardized word order or (2) a traditional word order can look weird to native eyes.

Note that when the PRC standardized its stroke order, it ended up with stroke orders that differed from calligraphic tradition: most notably 右 and 必. In addition, different calligraphic styles and regional variations sometimes have different character variants and different stroke orders.

In short, whereas there are a few mainstream ways to write words in Chinese, just like how there are a few mainstream ways to handwrite disconnected Latin letters, there are many variations that one is expected to be able to recognize, just as how one is expected to recognize a wide variety of Latin letterforms (copperplate, Palmer, blackletter, closed vs. open a/g, etc.)