Do amdk say in USA or England bother to trace their heritage? Maybe some but most don't even though almost all of them have roots elsewhere. The English not really a race a mixed from the early Vikings, then the Greeks, Romans and so forth, latterly the French, Spanish and Germanic influences. Americans don't say basically all descendants of immigrants
If really wanna look at Singapore, the first known people were actually from the old Tamil Kingdom of Srivijaya (I think). Hence Parameswara was actually a Hindu before he became Sang Nila Utama. The Malays being a mixture of Indonesian tribes like Javanese, Bugis even Sri Lankan - yes there's actually a Malayesque community in Sri Lanka to the present day.
That said if your family has roots here for over 50 years or more, say from just before pre-independence (1965) or self government (1950s) then more or less our roots are here. I have roots here (2 families) 1 going back to 1890s thereabouts the other 1950s. And while I would always like to visit either Sri Lanka or India as a tourist, I have no interest in my heritage from there, as being representative of who I am today and for the future.
Certain political, religious and cultural things from there may interest me but it's not crucial. It's the future that beckons and Singapore's future looks terrible. It was much better when I was growing up, to build a country that provides equality and opportunity for all.
also compensate me for occupying my ancestral lands so many decades too. 
