Most (but not all) single phase inverters I've worked with would operate at either 240 or 208 with a neutral, because the phase angle would tell them which nominal voltage is the correct one. Some, but not all, could be reprogrammed to work without a neutral.
If you have an inverter that requires a neutral, then in a high leg delta you have two line-line phases that don't have the correct relationship to the neutral. So you can only backfeed the phase that does, and have an unbalanced output. In a 208/120 wye you don't have that problem, because all L-L phases have a consistent phase relationship to neutral.
None of this speaks to the more theoretical questions upthread of whether backfeeding without a neutral could work in theory. It's practicalities of equipment engineering and meeting product standards and I guess manufacturers choices of how they want to support their equipment.