No, we don't.
Back in the 1960s, there was an experiment called ITA (Initial Teaching Alphabet). This was a modified writing system, using Latin characters and other phonemic symbols, in which there was a 1:1 relationship between the letters on the page and the sounds of the words - an attempt at phonetic transcription of the English language. The theory was that children would learn to read and write using this simplified system, and then they would adapt and learn the irregularities and complexities of 'real' English later on. The scheme was a complete failure, and the experiment was never repeated.
Schoolchildren in English-speaking countries begin to read with letter combinations that are fairly regular - cat, hat, sat and so on - and then gradually learn the irregular forms and exceptions later. As the failure of ITA showed, efforts at phonetic transcription just get in the way and confuse. Why burden children with learning a 'metasystem' which they will never use?
By the way, it isn't true at all, from our point of view that 'Auf Englisch spricht man Wörter anders als schreibt'. On the contrary, from our point of view, English words are pronounced as they are written. We just have an awful lot of overlaps and exceptions to rules.