are you suggesting that the spelling in those words - (he, she, me, we, be) - doesn't represent the same sound as the spelling in ego, evil, female?
Of course not, but that is an usual role for -e at the end of words. There are a few others (e.g. simile, epitome), but it's main function as a final letter is to lengthen the preceding vowel (female, tale, sale, pile, mile....).
"He, she, me, we, be" need special attention, because they are unusual, just like "the". To claim that they obey a 'code' makes no sense, unless u abuse the normal meaning of code.
I have also checked out when 'synthetic phonics' first came into established usage. - In 2005, after the publication of the Clackmannanshire study which contrasted 'synthetic' phonics with 'analytic'.
In normal usage 'synthetic' means:
artificial, fake, man-made, pseudo, sham, etc.
All pretty good words for describing the claims which SP advocates make about English spelling, as u did only a few days ago:
English spelling is highly regular - any spelling is regular if it appears in more than just one word.
A clear case of using the word 'regular' in way that is very different from normal usage.