'utopian-inspired' is a compound of 'utopian' and 'inspired'. 'utopian' derives from 'utopia' (coined by Sir Thomas More in 1516), ultimately from Greek ou- + topos meaning 'no place'; 'inspired' comes from Latin 'inspirare' meaning 'to breathe into'.

'utopian' developed from the noun 'utopia' (from Thomas More's work) into an adjective meaning 'relating to an ideal society'; 'inspire' passed into English via Old French from Latin 'inspirare', and 'inspired' is the past participle used in compounds. Together they formed the modern compound adjective 'utopian-inspired' to describe things influenced by utopian ideas.

Originally, 'utopia' literally meant 'no place' (a fictional ideal) but came to mean an ideal or perfect society; 'inspire' originally meant 'to breathe into' and shifted to mean 'to influence' or 'to stimulate creatively.' The compound now means 'influenced by idealistic/utopian ideas.'