I think there is stretching of scant facts on both sides of this debate.
Personally I buy the Sub-sector navies approach, in part because I read the scant evidence that way, but mostly because in my opinion it fits the underlying principles of the 3I well. That is, feudalism driven by slow communication/travel times.
The decentralized control driven by lengthy communication lines means Imperial control of the IN is slow. Giving local IN control to Sector Dukes is fraught (IIRC Norris took two years to get the authority and it required a personal appeal to the Emperor). History has numerous examples of outlying "Dukes" marching to "Rome" with Imperial forces loyal to the Duke (deliberately avoiding references to unpalatable alternative reality 3I history). Local IN leadership have briefs to protect Imperial trade but not engage in local politics except to enforce loyalty to the Imperium (typically by gunboat diplomacy).
Meantime, Planetary, Sub-sector and Sector leadership on the fringes of the Imperium recognize they exist on the front lines and those on the front line are often sacrificed in the slow dance that is main fleet maneuver. In practice this means no response from the IN if they are threatened by Alien fleets (unless it suits the IN). To the IN, the attack is merely another data point among many.
Having local forces available, dedicated to preserving the local political and economic leadership has a range of benefits up to the point of main fleet invasion by an Alien fleet (which politicians will always hope is the IN's job).
Are these local fleets a threat to the Imperium? In short no, they are dedicated to upholding a power structure that gets its authority from the Imperium. In turn they get access to surplus ships and other resources. Nearly always at lower tech ranges than the IN, yet potentially (if they can afford to maintain and staff them) on a par with Alien threats which are all at a lower TL than the IN. Should a local navy get too big, the IN can requisition ships from it for "special missions" or failing that, schedule a fleet exercise to visit in a year or two with a couple of BB Squadrons plus support.
Local forces in the meantime can be used to enforce customs, policing, prevent piracy and Alien marauders, influence local politics and economies (local gunboat diplomacy). The Duke with the strongest Sub-sector navy has an advantage when seeking to be Sector Duke (only one factor though).
The IN in the meantime retains the authority to commandeer local forces in the face of an Imperial threat. In practice however local fleets will typically do what the IN would want of them anyway. Harass Alien forces, slow down the advance, turn worlds into fortresses, tie up valuable Alien Fleet elements, repel marauders, provide intel to the Main Fleet, potentially be an anvil to the IN main fleet hammer.
Where the IN would take direct control of local forces will be in Sectors adjacent to Sectors under threat. Pushing these local forces towards the Alien Fleets to increase pressure and pin them down, without prematurely using IN Main Fleets. IN Main Fleet strikes have to be decisive, local forces not so much.
This will also influence the make-up of local forces;
- Planetary forces will prefer custom (non-Imperial standard) Fighters, SDBs and Monitors. Two reasons, the IN cannot commandeer them and they will fight to the last. Side benefits of aiding the local economy and increasing political status.
- Sub-sector forces will prefer jump capable fighting ships up to Cruisers. Low jump ranges preferred as they allow more fighting power per ton than a J4 IN fighting ship. Larger ships are too expensive to maintain and overkill for most Sub-sector jobs. A solitary hand-me-down BB would not do much against an Alien Fleet and would likely be tasked with keeping station over the Sub-sector capital anyway. There would also be a high chance of the IN commandeering it to do something useful which would be politically embarrassing.
- Sector forces would draw from Sub-sector forces (meaning Planetary and Sub-sector forces have two "friendly" threats, the IN and the Sector Duke). In this context a Sector force would not exist in peace time, in war time it would form around the Duke's Sub-sector navy. The Sector Duke may seek to influence the construction of local forces, for example, promote a local 80 ton advanced Fighter (incompatible with the IN) to Planetary governors who then maintain them as part of the Sector reserve. The Sector Duke may also seek to maintain a hand-me-down BB or two (s/he has a high chance of resisting the IN requisitioning them).
The alternative theory is that the IN does everything and local forces do not exist. This is less feudalism, more fascism which would likely devolve to feudalism anyway as local leaders take advantage of political and naval strength to carve out mini empires in order to resist unpalatable decrees from a distant Despot. Feudalism as constructed by the 3I accepts mini-empire building, but with the threat of the IN to keep Sector Dukes loyal and listening to the decrees from the distant despot.
On the lack of focus (evidence?) on local navies, the IN has always been the sexy service with the coolest toys and any Imperial naval service that is not the IN is sidelined. Perfectly normal, there are lots of books on the US Navy, not so many on the NZ Navy and I bet very few of those books on the NZ Navy are sold outside NZ.
Just one persons 2cr worth
YMMV.