They way I intuitively think of intertia, lies in the relation between the rating of confidence of information of reality, and how that implies for the resistance against changes of the same.
I personally expect an understanding to come from a revision of the foundational issues in QM and QG, where the the notion of intrinsic relational information capacity relates to a sort of inertia against exposure to contradictory information/feedback. And those generic questions has as I see it has nothing specifically to do with string theory, even though I'm sure this gets a "special perspective" within the framework of string theory, but to what extent it's an explanation perhaps depends on your own questions.
My only personal remote connection so far to strings is that string like structure might appear from a more fundamental thinking as evolved self-stabilised structures in a _continuum limit_ - possibly even the simplest possible non-trivial contiuum structures beyond a boolean state? But if that is so, strings doesn't seem elementary, which questions the entire starting point of string thinking, and thus while a possibility, I don't see if as an obvious or sensible starting point. And at least in my personal reference, if this is so, then the actual "key to inertia" seem to exists at a level more fundamental than the string themselves.
As far as I know this isn't understood yet? at least I don't understand it.
I think intertia is related to "stability" in general. And when one considers relative stability of different subsystems notions of internal time with be a local paremetrization of expected changes. I find this plausible, but where the intertia of different parts plays a key role. If one consider some abstract diffusion in information systems, it's seems to be a direct, and plausible association to connect "inertia" to information capacity.