The FAO lists Monostroma nitidum, Capsosiphon fulvescens, Codium fragile, Ulva spp, Caulerpa spp and Chlorophyceae as the most produced green algae in the world. And as you say none of them have a GRAS notice.

I think this is because the US produces close to none green algae according to the FAO, neither does it import any green seaweeds. So most likely the FDA has no intention to produce a notice, specially if noone is interested in to sell it in the US.

Global seaweeds and microalgae production (fao.org)

Also, I have read previously that there are multiple reports of deaths due to the consumption of green algae, so it could be a possibility that the whole biomass is not safe as it is.

Full article: Toxicological effects of marine seaweeds: a cautious insight for human consumption (tandfonline.com)