"To be fair they've done some bits of the NEPN several times already this year,"
This is part of the problem - the walk/cycle 'network' is dealt with by the 6 Neighbourhood Partnerships. Each has different overall priorities (quite reasonably as that's the point of 'local') and different lengths/types of path. The Meadows is not the same as The Innocent.
The section currently being cut (and allowed to overgrow every year) is looked after by South Team - same as The Meadows.
The other part of the Innocent (east from DRW) is maintained by East Team. Might be logical for the whole length to be dealt with by one Team - though vehicle access is a slight issue for the 'top half' because of the historic bridge.
However if CEC used (things like) 8 Freights there would be no access problems and they could easily transport strimmers - which might be more appropriate for regular maintenance.
Pedal powered maintenance vehicles would send a good 'message' and probably be more cost-effective than sending the large litter lorries along (relatively) narrow paths.
I have argued for years (probably since Lothian Region days!) that there should be a central point for the responsibility of the whole 'network'. In those days bits were dealt with by 'transport' (generally the old railway lines) and 'recreation' - which often had narrower and more poorly surfaced paths, not always appropriate in 'cycling as transport' terms.
Other paths were the responsibility of 'housing' which were generally (understandably) seen as pedestrian routes. Since the Access legislation it's not so simple - or perhaps more simple as it's now legal to cycle (almost) anywhere (RESPONSIBLY).
A lot of this all came together when CEC created SfC (some advantages lost by the devolution to NPs), but there still seems to be a gap between expectations (and funding) for creating and maintaining paths seen as 'transport' and 'leisure' - look at the various bits of the WoL and Braid and Burdiehouse Burns 'routes' and compare with the NEPN and Innocent. Some of the differences are due to benefit of building on former railway lines, but not all.
The spine through Craigmillar Country Park shouldn't be whin dust (for buggy pushers and wheelchair users, not just cyclists), but it was done 'to preserve the rural character'.
With the increasing amount of cycling (see yesterday's household survey!) and gradual expansion of the "Family Network" perhaps it's time for a better overview and oversight - unified policy and delivery of a genuine 'walking and cycling network'.