The approach is the right one for small genetic variants. But it will be hard to handle more complex kinds of variation without adapting the alignments to training example synthesis.
I think the field should cool it on calling the results of something like deepvariant "genomes". These are genotypes, not fully sequenced and reconstructed genomes. The evaluations are typically on easy regions and we have no reason to believe that those are the only ones that are important. One important tool to dig into this is syndip, which is a simulated synthetic diploid where the full haplotypes are known. It is a mixture of two haploid human genomes that were de novo sequenced with pacbio technology. (https://www.biorxiv.org/content/early/2017/11/22/223297). For the curious these haploid human genomes only exist in molar pregnancies, so even this isn't ideal but it is maybe the best resource we have at present.
GATK is still the standard, not because better variant callers don't exist, but because it's more important that everyone uses the same tool for comparisons between studies.
It's actually possible that DeepVariant is implicitly learning some of these correlations (1). This would make it really really bad for picking out the rare persons that don't fit a trend (and tend to be very important for identifying disease loci). GATK definitely does not know about correlated SNPs.
(1) The paper implies this is not the case, saying that DeepVariant works for other genomes without retraining, but they don't show the relevant results.
Obligatory reference: https://xkcd.com/1831
