I would guess that we are about a decade away from whole genome sequencing (WGS) being used *routinely* in cancer care, but in specific cases it is likely to be used sooner. The reason is that WGS doesn't currently give you a lot more diagnostic / prognostic value than sequencing a panel of a couple hundred genes that are the most frequent drivers of cancer. For cancer, you need to sequence very deeply to detect mutations, since they are not present in every cell of the tumor, and moreover, cells from a tumor biopsy also frequently include normal tissue (e.g. infiltrating blood & vascular cells). To get a good picture of the whole tumor, you also need to sample multiple regions of a tumor, or you will miss relevant mutations. It is typical to sequence both the tumor and a normal blood sample, so that you can be sure mutations you identify are not simply germline mutations (presumably non-pathogenic). Deep sequencing (>100x depth) of a whole genome is still very expensive relative to other tests.

Another reason that WGS isn't needed yet is that when mutations are found in genes that aren't yet strongly associated with cancer, it's hard to know what the significance is. Therefore, a lot of the cost in WGS would go to waste.

I could actually see RNA-sequencing having utility sooner than WGS, since that allows discovery of fusion genes, and is much cheaper than deep WGS. As data accumulates on variables associated with cancer prognosis, other genome-wide techniques may become useful. For example, epigenetic signatures (DNA methylation, nucleosome information from circulating tumor DNA) may become routine, since they can give information on the cell of origin, which can inform therapeutic decisions. It may be that histopathology won't go away for a long time, because it's a phenotype that isn't measured at all by genomics. Checking the histopathology ensures that you aren't completely missing something that genomics doesn't tell you.

Genome sequencing is widely used in precision medicine, but for a individual who carries one gene used to predict a typical cancer does not mean he/she has got this cancer. There are bunch of ethical and regulatory barriers or issues need to be solved or cleared for replacing current diagnostics with genome sequencing technologies in cancer care. Personally, I don't think it is possible that genome diagnostic technologies will replace current cancer care model in the next 10 years.