That is not a correct, Ameya. The wise care about things of the Samsara, they care about their duties. Only that they are not looking for any personal benefit, they are not inactive. - "Ma karma-phala heturbhuh, ma sangostva akarmani"
You are absolutely right in the sense that it matters for the sake of those for whom they are guardians.
And that is exactly what I meant by "they don't care" ,
it is not for their personal interest, they are simply doing their potentially minimal duty in the world. Wealth is needed for security of the family while a bare minimal comfort such as food, shelter are needed for the muni as well.
They are detached, yes, but especially in the context of this shloka, the munis really do not worry about many many elements of this world that are very important to others.
We are not necessarily talking about money as such, even that may have to be earned for the family, but more like social aspects - that many feel are an absolute must-have, such as a good impression in society , among friend circles, relatives etc. that people should say good things and treat them well.
That no one should misunderstand them. No one should laugh at them. These are basic human feelings.
The desire to belong, the desire to have a good social image, honor, people should call them smart and not dumb, silly, clumsy etc.
The muni in this Bh. Gita shloka 2.69 is focused on paramAtmA (tat padArtha : day for the muni) which is not on the minds of most others (night for the muni - honor in society etc.). This is also partly why some prefer solitude to society.
I just realized as I am typing this, that ---
This shloka is also alluding to the fact that you cannot fit 2 opposite-facing must-have swords in the same sheath while a nice-to-have sword may fit in.
i.e.
Self-Realization and ego are 2 swords that cannot fit in the same sheath.
Amazing how Bh. Gita realizations never stop. Something new each time.