By the way, it's not like other languages magically happened to avoid the same problems - from what I see looking at 19th century European text, they had the same issues that English still has.
Most of those languages have made a spelling reform or two that did exactly the proposed radical changes to spelling of words, including common words, to make spelling mostly match pronounciation.
The Atlantic article discusses the shenanigans of Belgian printers inserting unnecessary letters into words, changing e.g. "frend" to "friend". Spelling Reform 1 (SR1), a failed effort from the late '60s and '70s, would have addressed that and more.
Noah Webster -- of Merriam-Webster Dictionary fame -- spearheaded early American spelling reform. This is why American English writes "favorite" instead of "favourite", "center" instead of "centre", "catalog" instead of "catalogue", etc.
Other languages don't just have spelling reforms, but they also have institutions which periodically update the spelling of words.
For example, in Spanish, "Iraq" is spelled "Irak"—but only as of 2010! The change came with justifications: that it avoids the use of "q" outside of the digraph "qu", and that the terminal "k" is nowadays more familiar in words borrowed from other languages.
Japanese is a famously difficult language, but in the past century and a half, they've had multiple reforms which standardized and eliminated characters—there are more changes in the works, but it looks like they'll get new characters, such as "gaiji".
You don't want to learn Kanji, there's about 2000 of them for words and they have several different readings depending on context. At least you can guess the reading of some English words when you read them.
I like how there are two ways to say "I have a headache" in Japanese, and they are written with the exact same Chinese characters, but are pronounced completely differently:
"我有頭痛" sounds very Taiwanese. This usage of 有 is an artifact of Taiwanese / Minnan dialect. The Standard Mandarin （普通话） way to phrase that sentence is just "我头疼" or "我头很疼". Also like you said, 疼 sounds a little more mainland and 痛 sounds a little more Taiwanese. A general word for "pain" is 疼痛, they are really synonymous.
You can also guess Kanji readings just by looking at them. The largest class of Chinese characters consists of the "phonosemantic compounds", which consist of a phonetic part (how to say it) and a semantic part (what it means). Over 90% of Chinese characters fall in this class, but I'm not sure what rate you'd encounter them in Japanese. You can start doing this fairly well once you know... I'm not sure... probably in the vicinity of several hundred characters.
Several different readings is a bit of an exaggeration, it's more common to just have a kun'yomi and on'yomi reading, and on average I think the number of readings you'd know for a character is between one and two.
Purely from personal experience, I hear adult native English speakers (including myself) mispronounce words all the time! It's a common mistake to pronounce a word as if it were borrowed from e.g. French when it was really borrowed from Greek or Latin. So if you want to know how to pronounce "ch", you might say /ʃ/ if it's French and /tʃ/ if it's English. This seems to me like another variation on the same problem we have with reading Japanese, where characters have Japanese and Chinese readings.
My Consultant said when I was diagnosed with dyslexia that in countrys like Italy where the langauges are very regular there is less diagnosed dyslexia as the language makes some tasks esier.
Most of those languages have made a spelling reform or two that did exactly the proposed radical changes to spelling of words, including common words, to make spelling mostly match pronounciation.