That's exactly how the DNA sequencing works for fresh samples. https://en.m.wikipedia.org/wiki/Sequence_assembly We don't have the technology to do more than a few thousand bases in one go at the moment, so all modern sequencing means chopping up the sample, analysis, and then statistics based reassembly.

I don't know how it relates to million years old samples though. Maybe someone else knows why that's not easily applicable. I'd guess degradation being pretty random leaves chunks which are too small for analysis. (pure speculation, please educate me)