I think what you mean, OP, is: are Graeco-Latin stems the only stems from which compound words can be formed in English.
The answer is of course no: there are plenty of compounds in English based on indigenous Germanic words, and there were all the way back to Old English. Statecraft. Breastfeed. Windmill.
There was a preponderance of Graeco-Latin stems for scholarly and learnèd compounds through the Renaissance, and up until the last couple of generations. Not any more: Bubblesort. Backbeat. Widescreen.
And you really don’t want to see how Greek renders object-oriented as a single compound.
Ok, you do: αντικειμενοστραφής. “object-turning”, where object itself is “opposite-lying”. Daft, just daft, and not idiomatic. HY-252 “Αντικειμενοστραφής Προγραμματισμός” (Crete Uni, CS-252) shows what could have been: the OOP course is subtitled οντοκεντρικός “entity-centered”, which is, well, at least less daft.