It is beyond the point of debating whether there is a need as I have already started the process by submitting all of the other required documents and paid the fee (which is required at the time of application submission).
Many others who posted here about this topic before also has other passports such as those NZ and Canada, which is why this problem exists in the first place. And yes, BNO doesn’t give right of abode in the UK, let alone the EU.
I will try to get my name order changed on my HkID with just my US passport and see if this works.
Thanks!!