Does it prevent someone from getting permanent residence status as a spouse? I don't think so, at least in every case. But overstaying a visa for even a day results in a 3 year bar, so go home during the process. Apparently waivers of the 2 year requirement are harder to get when your J1 program is paid for by government.
https://www.lawfirm1.com/j-1-visa-to-marriage-based-green-card-rules-and-restrictions/
And what would be so bad about starting married life and a family in a foreign country, giving yor children dual citizenship?