I've not heard of Promethease before this discussion. It appears it will collect literature based on Single Nucleotide Polymorphisms (SNPs) in the DNA you send it.
Variant callers are a family of algorithms that look at the DNA in your sample and determine the SNPs. When thinking about coverage, quality scores assigned to sequence reads, and other pieces of information that may affect the variant caller, I would think about these inputs through their effect on detecting/classifying a variant. In other words, through metrics like accuracy, false positive rate, or false negative rate. State of the art variant callers are a little more complicated now, but simpler variant calling pipelines filter out variants that are of insufficient quality or read depth. This will primarily improve the false positive rate. If you are okay with casting a wide net in your search for a diagnosis and acknowledge that you may be seeing more false positives, then it's okay to go with a lower coverage assay.
As other commenters have pointed out, 30x coverage is widely accepted for germline sequencing. This is in contrast to somatic sequencing, which is more often done in the clinic for conditions like cancer where we expect much more variation among the DNA in the sample. Since that is not a concern in this case, you are probably fine to go for lower coverage options.
Edit: spelling