But it’s not supposed to be extremely common to apply for a green card on an H or J visa. Those visas are explicitly “nonimmigrant” visas for people “temporarily” in the U.S. who have “no intention of abandoning” their foreign residence. Read the statute: https://uscode.house.gov/view.xhtml?req=(title:8%20section:1.... It’s subsections (a)(15), (a)(15)(H)(i)(b) and (a)(15)(J).
The people who thought of this are trying to return the practice to the actual intent of the law. The law was sold to the American public as a temporary worker program. It was not billed as a pathway for permanent residency.