And the foundations of those statistical approaches are built on heuristics and shortcuts.

For example, sequencing instruments include base quality strings in the output. Base qualities are estimates how likely the instrument got each sequenced base right. But most people don't want to store that much noise, especially when the actual data is highly compressible. So the base qualities get quantized using more or less principled methods that seem to work well empirically.

Read aligners make similar estimates of how likely they got the correct alignment for each read. Those estimates are typically based on simplistic models and a number of assumptions. There are two main components in the estimate. One is based on comparing the primary alignment the aligner chose to the secondary alignments it also found. Another is an estimate that the aligner didn't find the correct alignment, because that part of the sequenced genome is too different from the reference. The latter is obviously handwavy. And the aligner cheats in the former. Because people don't want to wait 10x or 100x longer for better results, the aligner gives up early and estimates how good secondary alignments it might have found if it had actually done the work.

And then there is variant calling. At some point, the state-of-the-art callers were statistical. But then people got better results with neural networks. Or at least the results were empirically better.