Is there any advantage to increasing the bit depth within Sigma?

Please pardon an ill-stated question by one who has been indoctrinated by decades in the analog domain, but...

24-bit resolution is generally considered quite the cat's meow in audiophile circles. 16-bit CDs were the pinnacle of sonic perfection a few decades ago, yielding a theretofore-unheard-of 96dB dynamic range. 24 bits extends this to 144dB, certainly more than our human hearing mechanism can use. But certain Sigma chips let us work with 28 bits, a good 24dB better resolution than popular ADCs provide.

Coming from an analog perspective, where high signal levels always guaranteed the best SNR, it's tempting to introduce static gain within the Sigma chip, just so all those bits are utilized and exercised. But does it help at all? If one is limited by ADCs and DACs with 24-bit resolution, is anything really gained by DSP-ing bigger numbers or, at the end of the day, once we're ultimately back in the analog domain, did crunching bigger numbers really buy anything at all?

Perhaps the answer depends on the character of the ADC noise floor, including any dither that may have been purposely introduced. But it almost seems analogous to converting one's US dollars into Mexican pesos (about a 26dB magnitude gain), then buying, selling, investing, banking, etc. and converting back into dollars again. Of course that analogy would be sabotaged by the typical fee for each currency conversion. But perhaps digital architecture also imposes a 'fee.' There is no free lunch... is there?