(I’d never planned to get into this, but here are a few thoughts on the current debates, from mostly a historical perspective. I may (or may not) wade into the theological argument more seriously later.)

1. It’s much more difficult to accurately portray the 4th century controversies than you’d like. That’s why it’s a whole field of studies in and of itself. What escapes a lot of people is that Nicaea in 325 solved very little. It did deal with Arius. However, it never fixed ‘Nicene orthodoxy’, nor finalised the debates that followed in its aftermath. homoousion did not become an important term until the late 350s. Athanasius isn’t as important as 1st year students think. ‘Lines’ between ‘parties’ are much, much blurrier than textbooks make them out to be. The Creed of Constantinople 381 is so different to Nicaea 325 that JND Kelly doesn’t think you can even call it a revision. For all this, I do think something called ‘Nicene Orthodoxy’ on the Trinity comes to exist. However, its emergence is late, its synthetic, its primarily Cappadocian, and it still contains theological variety within itself.

2. Whether it’s proper to speak of order within the Trinity or not, it’s not proper to tie this to gender debates or ecclesiology (in this case, what women may or may not do in churches). In fact, it’s probably heretical to make those moves. I can see why these moves have come about on both egalitarian and complementarian sides, but they are bad moves to make.

For example, some egalitarians have a theology that tightly links function to being. Woman are the same being as Men, and therefore you can’t exclude them from certain functions, without suggesting difference at the level of being. Therefore, they can’t conceive that in the Godhead there is any difference of function without difference of being. In that view, for the Son to submit to the Father would be Arianism – because it would imply the Son’s inferiority to the Father. That’s why some egalitarians are so committed to proving Eternal Functional Subordination wrong.

It goes the other way too. Ware, Grudem, et alii, are so committed to seeing functional differentiation between men and women, that they want to see it in the Trinity in order to ground their gender arguments.

These are both wrong ways to argue. Wherever you are on the gender and ecclesiology issues, just stop dragging the Trinity into it because you are making a mess of your Trinitarian theology and it’s not helping your anthropology nor your ecclesiology.
3. Reading 4th century theology accurately is really hard work. And systemic theologians and protestant reformation historians often do it less-than-well. Not always, but more than I’d like to see. It’s not that I think non-specialists in this field should just go home, but a recognition that they’re playing an away game would be helpful. The problem, as I see it, is a tendency to read 4th century debates in alien terms of their own frameworks, which gets in the way of reading these theologies on their own terms and in their own contexts.

5. Configuring the debates as primarily ‘Orthodoxy’ vs. ‘Arianism’ misses a huge component: Marcellus of Ancyra. While Marcellus was an early ally of Athanasius, his theology came to be seen as modalist, and the consensus of Eastern bishops was always against him. This tarred Nicaea with guilt by association, and Athanasius as well (though he was opposed for political reasons as well). The final consensus emerged as much from a continuing regard to exclude modalist and Marcellan theology, as it did from ‘defeating Arianism’; for almost all parties, Arianism was dead in 325, Marcellus was the problem moving forward.

The whole ‘Arian’, ‘Semi-Arian’, ‘Neo-Arian’ set of terms is now virtually dead in Patristics. Because after Arius and possibly Asterius, it’s just inaccurate to call other theologians Arian. This is a legacy of over-realising Athanasius’ importance, because it’s he who both constructs ‘Arians’ as the enemy, polemically, as well as champions Nicaea and homoousios from the late 350s onwards.

6. Nicaea wasn’t envisioned as offering a solution. Indeed, beyond being a council that deal with Arius and his heresy in particular, its participants did not give it the kind of status common today. As Sieben argues, the view of the Council itself develops over time, becoming only latter a confession of faith of enduring value, and eventually seen as embodying revealed truth that is essential to the church’s faith-confession. What’s most intriguing about Nicaea is its absence from the debates for at least 25 years following. It’s prominence in introductory church history courses, textbooks, and popular Christian historical imagination is in large part due to Athanasius later writings and his construction of ‘Arianism’ as a threat and ‘Nicaea’ as the solution.

7. With Ayres, I recognise that the range of options is more than just ‘eternal functional order in the Godhead’ vs. not. The danger, as I see it, of EFS/ERS is that it appears to create problems with divine simplicity and the will of God. The danger without it, is that it may be impossible to say anything about intra-hypostatic relations at all.