I disagree. I have relatively similar background as OP. I applied to ~45 programs this past year and received ~35 interviews - way more than I could possibly attend. These include the research-intensive west coast programs (e.g. UCLA, UCSF, USC, Stanford, UW) even though I have no ties to west coast whatsoever and didn't do any aways in that region. In retrospect I would probably have applied to ~25 programs.
But, you never know in advance how many interviews you will get, so it's always better to err on the side of caution IMO. I think if you apply to similar number I did (40-45) you will get plenty of interviews. You can always turn down interview offers, and this is not the time to skimp.
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