I went to a primary school that had lots of “old school” teachers, and I am so pleased they insisted on teaching us the rules of English spelling and using a combination of explicit instruction, rote memorization, and creative writing activities. I can still remember chanting “i before e except after c” and other such things, as well as being taught big words like syllables and stress, and doing exercises to show we knew what they meant, from age 7, I guess. Even now, those rules help. We also need to remember that whilst good readers can work out these things for themselves, weaker readers cannot - they do need to be pointed out to them.
Looking at your list of words for the first semester, I am going to jump in there and suggest that there is some confusion between learning vocabulary for spoken English conversation and learning spelling with the aim of reading. Whilst some of your words (the, you, he, she, a) are on the lists of most frequent words (American Heritage 150, Dolch 220, others (mother, father, English, Chinese, elementary school) are not, and neither are they words that a reading program would teach in the early stages. It is true, mother, father, English and Chinese are words that we teach in conversation class. However, is it reasonable to expect children in their first semester to learn (memorize) these in a beginning reading program?
High frequency words do tend to have that characteristic of not fitting the rules. If you keep in mind that only 13 words (a, and, for, he, is, in, it, of, that, the, to, was, you) account for more than 25% of the words in print, and that the 250 words make up 70-75% of all words children use in their writing, it is worth getting those lists and learning the strategy to teach them, by rote and through association, as part of the reading program.
As for the other words, I really think it is one of the issues with bushiban classes. Conversation texts teach conversation, but many schools use these words as spelling words, too, when really there should be a different kind of program for reading. The result is we teach the words that are the exception, before those that are the rule. So I do understand your problem with some of those other words! However, you can use them another way. You can focus on the regularities within the words and use the words given to teach those regularities to children.
Also, be a bit careful - things are not always what the seem. “Child” is actually the long i sound, and there are a whole lot of words that belong in this group of common long i (bind, blind, climb, find, grind…) I am also pretty sure “School” is not “ch” but “Sc” plus the “h”. H is silent when followed by the “k” sound, like “sc” in school or “k” in khaki.
I also am wondering, why should “father” be an “o” sound? And isn’t “elementary” in the same group of short e as “elf” and “elm”?
So, basically, is your problem perhaps not that English spelling makes no sense, but that your school’s spelling program needs some reconsideration?