It's a good question. I've got two guesses. One is that, right now, it's very hard for big cab companies to enter the D.C. taxi market in the absence of meters, since there's no easy way for a large company to monitor its drivers under the zone system and see how much they're making. That has partly helped independent cab drivers flourish. Scrap the zone system, and suddenly the big boys will start moving in.
I can imagine someone thinking this, but it doesn't make a ton of sense. There aren't some huge economies of scale in the taxi business that big companies could plausibly take advantage of to drive small proprietors out of business. The plausible story by which the owner-operated cab dies is that a restrictive licensing regime is put into place which transforms the taxi trade from a labor-intensive business into a capital-intensive one. And, indeed, such a transformation is plausible, since it's happened in America's other big cities. But it's important to understand that the most plausible constituency for such a move is current taxi drivers looking to restrict competition, so DC's cabbies really have it within their power to prevent this.
At any rate, in my reporting on these sentiments it's clear that differences of opinion exist among cabbies, and that anti-meter fervor seems much stronger among Ethiopian drivers than among others. Indeed, two different West African drivers have treated me to furious diatribes about the evils of the zone and their fervent longing for meters.