Correction, most CDMA phones don't support it, but if the phone has SVDO, it will. The only phones I remember having SVDO is the HTC Thunderbolt and Rezound. Verizon didn't advertise it, because in their words the quality wasn't great (voice quality suffered while using it and data was IIRC running at 2G 1xRt speeds, so horribly slow). But it requires the hardware to support it, which most OEMS didn't bother with it.
IIRC, the Thunderbolt was originally slated to be a 3G device, and SVDO would've given Verizon customers the ability to do simultaneous voice and data (something AT&T was beating up on Verizon with in their ads). But when they decided to make the Thunderbolt an LTE device, which meant you could do voice on 3G and data over LTE, SVDO wasn't considered a selling point even though the phone supported it. And as I said before, SVDO wasn't a great experience, where with LTE you had 3G voice and LTE data speeds, so it was a no brainer. Of course since their LTE network coverage was so limited, many people couldn't make use of simultaneous v&d because they had no LTE coverage, so SVDO would've been good for people not covered by LTE.
Just wanted to clear up the misconception.