Up until the late Middle Ages, English spelling (at least, as we reconstruct it) is not that bad. It is internally consistent, and, importantly, it varies from region to region, because they actually spoke different dialects from region to region. Yeah, the mute final <e> was an annoying way to indicate that a vowel was long, but you’re not left completely in outer space.
A sequence of bad things happened at around the same time in the 1500s.
Printing was invented, which motivated standardising spelling. And freezing it in time. Not as frozen as we now think, there was still plenty of variability, but the 1500s is the last time English spelling makes sense.
Unfortunately, the 1500s was a bad time to be fixing the spelling of English. It was halfway through the Great English Vowel Shift. It was at the start of a bunch of other sound changes, some of which were pretty radical. What happened to <gh> was nuts, which is why the pronunciation of <gh> now makes no sense.
(That <gh> was a /x/, like the <j> in Spanish. So throughout used to be pronounced /θɹuːxuːt/. Seriously.)
And as if that wasn’t bad enough, the learnèd folk of the English language rediscovered Latin and Greek. So they started attempting to spell words in a fashion more appropriate to their Latin and Greek roots. And occasionally, even getting it right.
Sounds kept changing; English spelling didn’t. They changed pretty recently. Cue Samuel Johnson:
I remember an instance: when I published the Plan for my Dictionary, Lord Chesterfield told me that the word great should be pronounced so as to rhyme to state; and Sir William Yonge sent me word that it should be pronounced so as to rhyme to seat, and that none but an Irishman would pronounce it grait. Now here were two men of the highest rank, the one, the best speaker in the House of Lords, the other, the best speaker in the House of Commons, differing entirely.
Philip Stanhope, 4th Earl of Chesterfield, won—which, I guess, makes Irishmen of us all. (That’s why Reagan is pronounced Raygun. And why the Irish have a cup of tay.)
But we didn’t change the spelling of great to match; we still spell it as if it rhymes with seat.
Why no spelling reform in English, then? Well, as English-language spelling reform says, it could have been even worse. There was some 17th century reform: we don’t use warre or sinne or toune any more. Webster did, well, some things in the US. But really, the opportunity was lost in the 16th century, and we do lack the kind of centralised control that made centralised spelling reform possible elsewhere.