On "Existential Intertia": how to respond to it? Some notes
(1) Something's existence is either self-actual or caused. If we claim there are two things, existence and essence, & that essence is not self-actually existence, then they lack a factor of identity: any unity they have is extrinsically caused. This follows, as Lagrange articulates, from the "principle of extrinsic sufficient reason" or causality (derived from the "principle of identity"), which states "that which something has but not according to its essence is extrinsically actuated in it". Note how it isn't just temporal change or movement that demands a cause; such change is just a more specific kind of the "multiplicity or diversity in the depths of every created being", which evinces a composition or lack of identity demanding extrinsic actuation.
The notion of an existence present "inertially" in a finite thing, which then doesn't need to be conserved, is the idea of "essence identical to existence" or "essence self-actual with respect to existence". It's the idea that God could make another God (another being whose existence is self-actual, not caused).
(2) EI is incoherent given the real distinction between act/potency, essence/existence... for to say something has existence without participating in it is to deny this distinction.
Then we are back to the challenge of parmenides against the reality of multiplicity, limitation, change: obviously if (say) plants are identical to existence or exhaust its possibilities, there would be no animals or artifacts (the only thing extrinsic to being [which apparently x is identical to to exclusion of y] is nothing).
There is no "demonstration" of this; demonstration is the reduction of two terms to a more basic or shared middle: "man is a rational, jim is rational therefore jim is a man". We can't run this argument with being as it appears in any major, minor & conclusion. It is self-evident that being is a "polyvalent form that actually & implicitly contains all things" (to paraphrase maritain/lagrange), which finite things 'have' only by participation .
The above reasoning instead constitutes a reduction to absurdity of the idea that being is not participated: people who deny this are forced to countenance some modernist variant of parmenidean monism, denial of the polyvalence or essential diversity of being (as between essence, existence, man & God etc).
A great example (of something resembling "existential intertia" or the idea that existence is intrinsic to not participated by finite things): in Judith Butler's "subjects of desire", we read that "natural multiplicity" is "unsupportable metaphysical speculation". Differences & telos, even the difference between physical bodies & idea of a subject of action, is "socially & linguistically constructed" atop homogenous physical reality.
In further response to this post,
The paper seems to reinforce my understanding of EI, in that you appear to be suggesting a metaphysics akin to the one I said above that EI precipitates!
While the question is deferred in the paper at some points, your case for EI (persistence in being without extrinsic causality) seems bound up in promotion of univocal or generic being & takes for granted possibility of essential absent ontological difference.
I'll do my best to comment on the parts that I am able!
This pictured bit particularly seems to gloss over the reason act/potency distinction is invoked at all: unlike a univocal genus, which can be diversified by extrinsic differences, being has no extrinsic differences. This means without different ways of existing, there can (we say) be no differences in kind or amongst entities: what diversifies them from global being & one another (but no-thing)?
The unavoidable conclusion down the road seems to be that difference (as between types or beings) is sub-real, maya-esque: "socially & linguistically constructed" atop generic ontological reality as i mentioned above (and even here, there is an ontological pluralism invoked, as between act-being-physicality & post-ontological constructions).
Meanwhile the idea that pluralism involves rejection of "generic" existence is true... but only half the story, leaving out why we can say everything is thus and so. There is an asymmetrical relation of comprehension (in terms especially of formal causality) between act-potency, the same kind of relation of a univocal essence exhibits re its individual instances. So while being doesn't generically or univocally or homogenously encompass its differences, this is because it is a higher order form or "superuniversal" as Maritain deems it; the "highest form of all, which actuates all things, even form" (aquinas). So it exhibits "transspecific, transgeneric consistency" & "actually & implicitly comprehends all things", like the "inexhaustible, liquid-crystal environment of metaphysical intellection". All to convey sense in which being is not MERELY generically unified.
If someone were to say (a Scotist perhaps, denying a space between univocity & equivocation) that being cannot be polyvalent, "above one & many", we must ask: why not? This is a question of metaphysical fundamentals no reference to logical machinery can solve (it has to do with what we say is real, simple, intrinsically-evident objects/"understanding", before we proceed build a structure of complex reasoning on its basis/"science" like logic).
This brings us to why we can't articulate act/potency as atomic or delineated "parts" of the same thing (something you described very well I think); causality whereby actuality is communicated is the "action of the agent in the patient". So like in the case of existence in essence, a creature can participate in or exhibit the actuality of an extrinsic agent, as creatures in God, without said actuality being theirs or a component of them. The relation is of act to potency, any other way of parsing it seems to obfuscate an ontological situation in name of something nominal or conventional.
The reason existence must be extrinsically caused & conserved (we say) is this relation of essence to it as potency to act. Granting ontological pluralism, actuality is always something extrinsic to potency which the latter participates in (& if any finite thing was self-actual with respect to existence, there would be no other things).
Meanwhile, granting univocity of being, existential intertia seems implied!