When the ESV says it is 'essentially literal'... emphasis is on "word-for-word" correspondence" - that allows it an exclusion clause for occasionally deviating from a literal translation. It gives to itself permission to use 'corresponding' words in its translation. Revelation 10:6 is one such example of the ESV not merely choosing an alternative word, but an entirely different word.
Many translators today will claim that chronos can include the idea of a limited period, so that 'delay' is warranted. Appendix 195 of 'The Companion Bible' (Bullinger) says:
(1) chronos, time, duration unlimited unless defined..."
(2) kairos, a certain limited and definite portion of chronos, the
right time or season..."
Consider that he word 'kairos' was not chosen by the angel speaking to John. Sticking with 'χρόνος' as does Robert Young, consider his rendition of the whole verse:
"...and did swear by him who doth live to the ages of the ages, who
did create the heaven and the things in it, and the land and the
things in it, and the sea and the things in it - that time shall not
be yet..." Y.L.T.
Interestingly, despite the YLT being consistently literal, the word for 'yet' does not appear in the text. Three times various Greek words for 'yet' appear in Revelation: 6:11 - et - still, yet, hitherto; 8:13 - mello - to be about to; 9:20 - oute - and not, neither, nor. This suggests that the best literal translation is, "that time shall not be".
Others would claim that it's speaking about 'prophetic time', though that clearly is an interpretation. Yes, χρόνος can include various meanings about time. That's not the problem. The concern here is that because most modern translators cannot fit the idea of time being no more into their theology, they have decided that the Greek word for delay should have been used, despite that it was not chosen by the angel. But 'no more time' and 'no more delay' do not mean the same thing despite modern translators trying to say there's no material difference.
To answer your main question: All this suggests that the ESV has chosen its choice of word, 'delay', for Revelation 10:6, on a doctrinal bias about their interpretation of time. Being time-bound mortals, that may be understandable (for who of us can mentally cope with stepping out of time, and entering eternity - which is what happens when we mortals die?) Eternity is God's domain, it has always been and will always be. But God created time for this material universe (e.g. it takes time for light to travel) and we are bound by time, for now. The very idea that we may be unbound, so as to exist where our concept of time gives way to God's reality of eternity, is enough to cause many to alter what Revelation 10:6 actually says, I would suggest.
To answer your secondary question, Is there something in the text that absolutely demands uniquely substituting "delay" for "time"?: There is absolutely no demand in the text for substituting 'delay' for 'time'. Quite the opposite - 'kairos' means a certain limited and definite portion of 'chronos'. So, the word 'time' stands purely and simply within the whole text as meaning 'time' (unlimited), and nothing else, otherwise the word for 'delay' would be there, somewhere. It is not.