Yeah, he could. But that was not in fact what he did. Gawker didn't lose by attrition, they lost a particular case they damn well deserved to lose.
On the other hand, Thiel says Gawker's former victims have been forced to settle for a pittance because of attrition on their end. That sounds entirely plausible.
Money matters in court, by default that favours corporations (including media corporations like Gawker, and their $200-million owner Nick Denton) over all but the richest of individuals. That's the status quo, now the media are upset that it didn't work in their favor for once.