We do have incidents of vowel harmony, although it is not so developed as to be a part of our actual formal grammar or phonology. I.e., there are no rules dictating it, but it does exist as a phenomenon.
One example that came up for me recently was when I did a reading for some people in Turkey of all places. :-) There was a sentence that ended, “… The“…the importance that owning a vehicle plays at every stage of life.” Somebody there objected to my reading of “at” as “et”. Yet this is what most speakers of American English would do except when reading very slowly and distinctly for a non-native speaker.
On the other hand, if the word “at” came after a low back vowel like “rows“row,” we’d pronounce it closer to “at.”
Contrast:
There’s a row at the back. There’s a tree at the end of the street. A tree Most
Most speakers will pronounce something closer to “tree it the end of the street.”
Because nobody does it deliberately, we rarely even think about it, but actually pronouncing “the tree at…” feels odd in exactly the same way as “Izmir’a” would feel in Turkish. (The correct form would be “İzmir’e” (“to Izmir”).