IF they can't recite posadha together [they can't], then what makes you think they can transmit vows together, and whose would they transmit? The reduced rule set of Theravada, or the expanded rule set of the other two?
Why can't they recite the posadha together? Language differences?
I imagine they would have to transmit the reduced set since all three would hold all the vows (again I imagine) contained in the smallest set.
They can't recite posadha together because the vows are given in different orders, and in the case of the Theravada vows, there are 30 o so less vows.
So what you are basically suggesting is that we scrap Mulasarvastivada and Dharmaguptaka. But if you do that, you will scrap the nuns vows in Dharmaguptaka, since they died out in the other two orders (and the reason for their dying out is a gender issue). If you want nuns vows in Thervavada and Tibetan Buddhism, either Theravada and Mulasarvastivada needs to be scrapped, or, things remain at the status quo i.e. nuns who want a valid ordination get that from the Dharmaguptaka lineage.
Someone mentioned that monks form Tibetan Buddhism and Theravada were present at these nuns ordinations -- yes, they were, but not as members of the required quorum. They were present as guests and observers.
Then there is the additional gender issue of the 80 odd extra vows nuns must keep in addition to the monks vows. This is unfair. But will these be scrapped? No. Should they be scrapped, no.
Are all monastic sanghas going to collapse in the next 500 years? Definitely.
Should we be sad? No.
Will there still be Buddhist practice even though the monastic sangha is no more? Yes.