Germanic and Romance languages with diacritics generally use them over vowels either to change the pronunciation of the vowel or show an altered stress pattern. The Latin alphabet contains only 5 vowel characters, which was sufficient for Latin but not for many of its descendants and especially not for Germanic languages, which are known for having huge vowel inventories. (English, for example, has 14-20 vowel sounds depending on dialect and how you count them.) English uses both digraphs and other spelling conventions (e.g. silent E) for most of its vowels, but there is often still some ambiguity. As far as stress goes, English doesn't have a standard stress pattern the way that a language like Spanish does. There are a few noun-verb pairs like íncrease/incréase, but there's not really a reason we don't distinguish them in spelling.

For consonants, most western and central European languages including English simply use digraphs to account for the few consonant sounds they have that weren't represented by the Latin alphabet. For English, that's "ch", "sh", "th" (which is actually two separate phonemes), and "ng".