BQSR is not needed since Illumina base qualities are quite good nowadays. But it is still a standard part of many reference alignment pipelines... because it's recommended by GATK's best-practices for DNA-seq. And it inevitably gets used in cancer genomics pipelines, where there are real variants at various allele fractions. And since these variants are not in dbSNP, they will be classified as sequencing artifacts that are used to generate the recalibration table - that inevitably "corrects for" these real variants - reducing sensitivity.
I still haven't done my test, so can't confirm this assumption yet. But does it make sense?
Looking ahead to the results for your test. I have observed a similar problem in regards with finding novel variants. The Base Quality Score Recalibration will probably decrease the chances of a variant caller to detect novel snps.