On such an account, there can be no spiration without generation and no generation without spiration. One can deny that necessary connection only if one argues that the Father just happened to originate two other persons, when he might as well have originated more, less, or none. I don't believe anybody is prepared to make such an argument. Yet there remains a sense in which the Spirit is "of" the Father and Son which is not the same as that in which the Son is "of" the Father and the Spirit: the Son is the perfect self-expression of the Father, which is not said of the Spirit too. Thus the Son is logically but not ontically prior to the Spirit. That accounts for the traditional taxis of the divine persons; but on my account, it does so without subordinating the Holy Spirit.
The chief objection to such an account, as far as I can tell, is to cite the Cappadocian principle ('CP' for short) that every divine property must be either individual, and thus unique to a particular hypostasis, or common to all three and thus "of the nature." If CP, then origination ad intra, in any sense of 'origination', must belong to the Father alone. And I have observed CP repeatedly invoked by Orthodox commenters against the filioque on any construal of that doctrine. Hence there is no originating within the Trinity that is not ekporeusis, and the filioque is incompatible with DMF. From that, it follows further that the Son and the Spirit each have no role in each other's origination as persons; their interrelation is thus purely "energetic," having nothing at all to do with their "hypostatic" origination from the Father; hence the Holy Spirit proceeds from the Son only energetically not hypostatically. Now as I've said before, I've never found that result plausible. We do not say merely "God is loving" but also, with the Apostle John, "God is love." So, granted that the divine persons are necessarily as well as mutually perichoretic, it hardly seems plausible that the hypostatic origination of each originated person has nothing to do with that of the other. But that's what follows if CP is true. So then the question becomes: why believe CP?
The most common argument for CP I've seen is the sort of reductio deployed by Patriarch Photius in the Mystagogia: on the supposition that CP is false, there could be infinitely many divine hypostases, which is absurd as well as heterodox. But that argument is entirely question-begging. As Jonathan Prejean points out, St. Anselm's argument in the De Processione Spiritus Sancti "can quickly be used to demonstrate that, if there is more than one Person, there can be exactly and only three based on the bipolarity of the relations, and Photius's reductio doesn't work on it." It is highly unlikely that Anselm knew of the Mystagogia, but the point stands anyhow: the only way to block Anselm's argument is to premise that the only sort of origination within the Godhead is ekporeusis, which by common agreement belongs only to the Father. But that kind of monopatrism, of course, is precisely what is at issue. To be sure, the assertion that the Holy Spirit comes forth "from the Father" was made by Christ himself as quoted in the Gospel of John and repeated verbatim in the Nicene-Constantinopolitan Creed of 381, accepted decades later by Rome as ecumenical. But the assertion that the Holy Spirit's origination from the Father in no way depends on that of the Son is a feature of one theological grid, the Cappadocian, among others. It is not itself dogma.
The issue, at bottom, is whether DMF logically depends on CP. I agree that Anselm's argument shows it does not. For a fuller exposition, see Prof. Scott Carson's paper "And the Son" given at an ACPA meeting last fall.