Your definition of the Borg semantically proves the point.
The Borg attempt to accomplish this by assimilating various species
Assimilating. Not supplanting. They are integration the species, which inherently means keeping some of the species as part of the Borg-assimilate.
and augmenting them with cybernetic implants.
An augmentation is supplementary. It improves on the original.
You can't have an augmentation without having the original (even if it's heavily altered).
If the Borg were purely synthetic, there'd be nothing left of the original, and therefore they are not augmenting species but supplanting them.
However, when the Borg assimilate an already fully synthetic species, that those particular Borg will be fully synthetic as well.
However, due to the nature of biology, no biology is perfect (all biology eventually ages and dies), the Borg in its current state cannot survive without functional biological components. Meanwhile synthetics and technology don't have the same limitations;
You're making a few too many assumption about Borg lifespans here.
It is not confirmed that a Borg-assimilate has a lifespan equal to or somwhere near the original species' lifespan.
Also, biological components have a very similar replacement method:
a malfunctioning implant can easily be repaired, upgraded, or replaced.
Biological cells do this all the time. It just happens that the lifespan of a biological cell is less than that of a synthetic component, but the principle of swapping out the faulty parts remains.