I don't think any sports puts individual over nation other than Golf. Most of these athletes would have probably chosen regular 9-5 jobs had the honour to represent their countries not been a factor.
There's tennis too. For e.g. Sharapova is often said to be a Russian tennis player but isn't she based in the US?
I think with the current structure of badminton/BWF especially with the prize money and sponsorship opportunities available it's impossible to transition to a model like tennis. Instead players have to rely on their national teams/training centers etc which of course can only feed into the identifying players based on nationality mindset.
She isn't an immigrant, just an expat. There are many US, Kazakhstan or Aus based immigrant players who represent US, Kazakhstan or Aus. MaSha aint one of them. She is a proud Russian, an active supporter of Putin, never misses a Fed Cup or an Olympics and wears her Russia colours very proudly. Admittedly her spoken Russian is poor and she has a heavy accent, while her English is impeccable (which at times is a cause of resentment amongst her own fellow Russian players who are relegated to the bench due to her.); but the only reason she is in USA is because of tennis (IMG-NBTA was better than any Russian academy in the 1990s and Yuri, her dad wanted the best for her.) Infact don't be surprised if post retirement MaSha joins Safin in the Duma (the Russian parliament/congress) Also for every tennis immigrant like Navratilova/Hingis/the Rodionovas/Shvedova/Nedovyesov/Karantatcheva/Lepchenko you will find badminton equivalents like Pi Hongyan/Mia Audina/Yao Jie/Biewen Zhang/Xu Huaiwen/Zhou Mi/Wang Chen/Lim Xiaoqing/Hu Yun... And guess what just like badminton emigres compete fiercely for their adopted teams, the tennis travellers are equally passionate in DC/FC/Olympics in addition to the regular tour. Infact the French Davis Cup crowds might dwarf their Indonesian Thomas Cup counterparts. The comparision hold true Aus/China (Aussie Aussie Aussie Oi Oi Oi vs Lin Dan China Lin Dan China Li Xuerui China..... Long but hopefully helpful.