One of technology giants’ irresistible features—that their services are monetarily free—could inhibit antitrust regulators’ possible attempts to break them up.

A new antitrust task force at the Federal Trade Commission plans to scrutinize if past technology industry acquisitions caused anti-competitive harm. Critics commonly cite Facebook Inc.'s 2012 acquisition of Instagram as a deal that the FTC should have never approved given the social media service’s growing dominance.

The FTC, in reviewing already-closed mergers, is open to breaking up harmful technology...