Funny, I was going to say the opposite.
I took Chinese for a couple years, and while the tones can be annoying for the first few weeks, there's only 4 (or 5) of them. It ain't rocket science. If you can recognize the melodies of songs, then your brain has the necessary parts to recognize tones too. Nobody in any of our beginner Chinese sections ever found the tones "just not doable". Some people would take a few days to get the hang of them, and other people a couple of months, but if more than a billion people in China can do it, you almost certainly can do it too.
(And if you're really having trouble you can always hire a private tutor. Honestly, most people with pronunciation problems in any language, just need some individualized help. A group classroom might not do it, but one-on-one tutoring almost certainly will.)
On the other hand, most people simply don't have the time to memorize the characters and pronunciation. The fact that there are virtually no cognates makes the hurdle to amassing vocabulary simply gigantic, let alone the characters. You say that "anyone, with some work, can memorize the characters", but "some work" in this case is a truly gigantic amount of work.
I took Chinese for a couple years, and while the tones can be annoying for the first few weeks, there's only 4 (or 5) of them. It ain't rocket science. If you can recognize the melodies of songs, then your brain has the necessary parts to recognize tones too. Nobody in any of our beginner Chinese sections ever found the tones "just not doable". Some people would take a few days to get the hang of them, and other people a couple of months, but if more than a billion people in China can do it, you almost certainly can do it too.
(And if you're really having trouble you can always hire a private tutor. Honestly, most people with pronunciation problems in any language, just need some individualized help. A group classroom might not do it, but one-on-one tutoring almost certainly will.)
On the other hand, most people simply don't have the time to memorize the characters and pronunciation. The fact that there are virtually no cognates makes the hurdle to amassing vocabulary simply gigantic, let alone the characters. You say that "anyone, with some work, can memorize the characters", but "some work" in this case is a truly gigantic amount of work.