[ø] ≈ [ɯ]?

Is it just me, or does the vowel [ø] (a close-mid front rounded vowel) sound a lot like [ɯ] (a close back unrounded vowel)?

I first encountered [ɯ] when I studied Japanese (it’s the normal pronunciation of /u/), but I didn’t really think about it at the time.

However, when I learned Scottish Gaelic, I heard the vowel normally written as ‘ao’ (as in aon “one”) as [ø], but I subsequently found out that it’s supposed to be [ɯ].

When I then recently tried to find out how to pronounce Kim Jong-un (???), I first saw on John Wells’s blog that it’s /ɡ̊im d̥ʑ̥̯̯ʌŋ ɯn/ in IPA. However, if I listen to the last syllable in Google Translate (click on the wee loudspeaker symbol next to Ä), again it sounds very similar to a Danish /ø/ (it’s possibly clearer without the final n).

Are the two sounds really that similar acoustically, or is the Danish /ø/ drifting towards [ɯ]?

If they really are very similar, that could explain why languages tend not to employ both front rounded and back unrounded vowels at the same time.