I think it's the general consensus that white should enter d4-openings when facing d5-systems (i.e. transposing to the Queen's gambit) or King's indian set ups. White can play Reti lines vs d5 and KID positions with d3 (instead of d4), but chances for advantage are smaller. One way of meeting d5 is to transpose to the Catalan which is similar in style to the English and may offer more chances of advantage than the Reti. Many players who choose the English as white are quite happy to play roughly equal positions. Opening choices is more than searching for +=, it's also finding openings that suit your style.