Learn English – Are there regional distinctions in how hiccup/hiccough is spelled

Your assumption is correct. Natural languages are extremely redundant and compressible in sound as well as in orthography, and this has significant and obvious benefits: you can understand obscured speech, read obscured text, and, yes, get the sense of a word based on a quick visual hook rather than relying on a purely phonetic transcription.

English orthography reflects its countless generations of development. The spelling of a word may not correspond perfectly to its pronunciation, but to select a spelling that does correspond to a specific pronunciation naturally excludes some others. I've heard native speakers, for instance, who have different pronunciations for all of "to", "too", and "two".

Further, since the orthography often reflects the etymology, you can often make an educated guess about the meaning of a word you don't know based on the union of its visual and phonological components. If they were collapsed into one, you'd lose that extra information. This is just like how in hanzi there's often a phonetic component as well as a semantic component, and this does carry over somewhat to kanji even though the pronunciation is adapted to Japanese phonology.

These are all reasons why English spelling reform has never caught on, and likely will never do so. It's too widespread, and there are simply too many factors to take into account. Every language has its idiosyncracies, and to see them as flaws or try to fight them is sheer folly.

I seem to remember the old askoxford.com site said either was acceptable: CDs and CD's.

But now the replacement Lexico powered by Oxford firmly suggests to avoid the apostrophe except in a few special cases:

Apostrophes and plural forms

The general rule is that you should not use an apostrophe to form the plurals of nouns, abbreviations, or dates made up of numbers: just add -s (or -es, if the noun in question forms its plural with - es). For example:

...
MP MPs (e.g. Local MPs are divided on this issue.)

1990 1990s (e.g. The situation was different in the 1990s.)

It's very important to remember this grammatical rule.

There are one or two cases in which it is acceptable to use an apostrophe to form a plural, purely for the sake of clarity:

• you can use an apostrophe to show the plurals of single letters:
  • I've dotted the i's and crossed the t's.
  • Find all the p's in appear.
• you can use an apostrophe to show the plurals of single numbers:
  • Find all the number 7’s.

These are the only cases in which it is generally considered acceptable to use an apostrophe to form plurals: remember that an apostrophe should never be used to form the plural of ordinary nouns, names, abbreviations, or numerical dates.