Why did English spelling reform never take off?

First off, English has a rather complex phonemic reservoir for the Latin alphabet. We have about 20 vowels and 25 consonant phonemes (exact numbers depend on dialect and how you count them), yet our script allows only 26 one-character targets. 28 if you want to bring back þ and ð. Adding diacritics or new characters runs into the major problem of support, as anyone who's had to take a foreign language like France or Spanish while using en-US keyboards are all too aware. Indeed, þ was dropped from the language in part because of the lack of support in printing type.

A second problem is that phonetic spelling is somewhat vague as to what the goal is. Should you try to give only one spelling to each phoneme, so that you can perfectly spell given pronunciation? Or should you be able to predict the pronunciation given the phoneme? It's also worth pointing out that pluralization and verb inflection rely heavily on simple morphological rules (add -(e)s/-(e)d to the end of the word) which would be complicated by insisting on phonetic purity (note the 'z' sound in words like dogs or says). Demanding only one spelling of phonemes seems a bit harsh, especially if you're going to admit digraphs. I like being able to distinguish words like meet and meat.

Another problem is that there are some phonemes without clear representation. The 'th' digraph (retained in all spelling reforms I've been aware of) actually represents two distinct phonemes (say "Thy thigh" to hear the difference clearly). Of course, there is a very natural pair of letters to represent it, courtesy of Icelandic (þ and ð), but see above (also, people are liable to assume ð is approximately a "d" sound, which isn't right). The "sh" is natural to many people, but its voiced counterpart (ʒ in IPA) has no natural counterpart. The soft g or a j is a dʒ sound; "zh" crops up in some Romanizations of Chinese, but it's not attested in English; and the places where it does come up (e.g., vision) don't lend themselves to a natural borrowing.

Which brings us to the biggest problem of spelling reforms: they target the wrong thing. When showing off these reforms, there's often big hoopla about things like "-tion is pronounced /shun/ and that makes no sense!" whereas the s/tion/ʃun/ pronunciation rule is one of the most productive and least exceptional in the English language (cation is the only word that comes to mind as an exception, and even then it's not really an exception because the word is derived from cat·ion, so the -tion isn't really a group). The real travesty of English spelling is that we borrow words from foreign languages and reuse the same spelling and pronunciation. Words like gyros ("yee-rohs") or quinoa ("keen-wah") are absolute travesties and really should be changed in either spelling or pronunciation. But insisting that we must change "advise" to "advaiz" and "advice" to "advais" seems overly pedantic when they're perfectly predictable with standard phonetic English rules.

That's one final thing to bring up: English is already quite phonetic. http://www.zompist.com/spell.html gives a list of ~60 substitution rules to convert English spelling to pronunciation that covers ~80-90% of words. The main real travesties (in non-imported words) are a few vowel digraphs like -ea-, which has several pronunciations with no real rule to pick which one applies.