I disagree with this. On the surface, some letters are closer to others indeed, notably C and X, as you say but they still serve more purpose than one might think.
Without C we wouldn't have, for example, CH. Sure there is SH but those sounds are still different. Not in a massive way but consider the differences between S and Z. CK is also a thing as opposed to KK (which is used in certain more phonetic languages where the K sound actually is affected more).
As for X? If I were to say "Akses", am I saying Axes or Access? How about Xylophone?
Q? In order to even try to replave that with KO or KU we'd need to change the pronunciation rules are "Kuit" (Quit) would be pronounced "Coo-y-t" if spelled like so, almost sounding like a mispronounced "Cute" (which by the way, 'kute' would be 'coot' and not 'Q-te')
Not to mention that we are all so accustomed (akkustomed???) to the current rules of grammar, spelling and how the words 'look' as well as how other indo-european languages are built that it helps keep the letter count per word shorter as well as make these words a lot more readable and less 'weird' looking.
English isn't very much a phonetic language and relies on many rules such as grammar as well as word origins to a degree to explain how a word is to be spelled. It's not about ease of pronunciation as much as it is about encompassing a large number or words and maximizing readability.
I've even seen arguments saying that English could use even more letters. Many Germanic languages already do this with letters such as Å, Ä, Æ, Ö, Ø, Ð, ß, to name a few, Many of these correspond to sounds that are very foreign to English and even hard to pronounce for many English speakers out of the simple reason that they've never heard it before. In Swedish we use Å, Ä and Ö in addition to some other sounds like SJ which aren't at all really used in English. The letter R also is very different between languages; So much that if you would have all the different pronunciations in the same language you would probably need at least 3 different letters for just different R's.
Ok, first off, ku sounds nothing like kw, so I don't know where you're getting that from. Qu = kw.
Queen = kween
Cute = kyute
Axes = aksez (akzeez is how it would be written in British English)
Access = akksess
And for ch, /tsh/ is identical in pronounciation to ch.
There are few acceptions where tsh would not be used for ch
Chemical = khemikal
School = skhool
Anyway, I'm rushing to type this while a video is playing in class so, I'll explain everything in greater detail later.