That's impossible to some degree because English pronunciation varies so much across dialects.

Or rather, you could make writing phonetic but then spelling would have to vary by dialect.

I just realized it's done precisely like that in my language! Never even thought about it. But there is a standard "written" version of the language and dialects are mostly spoken.

Isn't that true for every language?

Nope. Most languages have no written standard, and some have more than one (E.g., American vs. British vs. Australian English, or Nynorsk vs. Bokmal Norwegian).

please specify the language so people can learn things, it's the internet

That's really hard with old languages. Accents and new words surpass the alphabets with time. Turkish for example switched to using Latin alphabet on 1928 and they were able to map every sound to a specific letter. If you know the Turkish alphabet song you can read every text with perfect pronunciation. There aren't even any letter combinations to consider, letters have one sound and are individual.

We have an alphabet that can be used to give something close to certainty regarding punctuation. ɪt wʊd biː ˈkʌmbəsəm - to begin with, but I’m sure we could get used to it.

I think I’d prefer it. I enjoy reading text which has been written ‘in an accent’, where the usual way is to bend the standard alphabet so ets cluen yer en aboot tha propa wuy ta sey et.

The problem here is that a vowel is split in some dialects but not others. Phonemic spelling would not solve this problem.

Okay, so you're saying we should just discard the centuries or even millennia of etymology encoded into spellings because it's better to make sure symbols on the page directly correspond to your preferred pronunciation.

In at least England, this would cause spelling to have regional variations. E.g. 'bath' in southern English is often pronounced as if was spelt 'barth' while in the North it would be 'baf'.

Not while using an alphabet with just 5 vowel letters. Switching to IPA would do the job, though.

5 vowels, and then 25 more vowel combinations (e.g. ea)

I don't think those 25 combinations are enough to cover all the cases of unique vowel sounds, diphthongs, and pairs of distinct adjacent vowels that you find in English. 'ea' for instance is ambiguous between sounds like those in 'great', 'deal', and 'creatine'.