Some more in depth feedback:
"There are also economic factors. The Imperial Army must arm millions of soldiers* – and also move them**, feed them, house them and keep them supplied***. There is only so much TL15 manufacturing in the Imperium.**** This would need to not only provide all the new weapons and equipment but also all the spares and supplies required to keep it working."*****
*Arming millions of soldiers is a drop in the bucket compared with the IN funding.
** They are mobile thanks to the IN, BatRons and Assault Squadrons carry the Imperial Army, their equipment, and theri logistics tail.
*** Which is what waystations were originally for "lmperial Way Station. A base established for the repair, maintenance, and overhaul of lmperial equipment. It may include provisions for Army troop barracks, naval and scout ship overhauls, and intelligence operations"
**** There is more than enough TL15 manufacturing capacity within the Imperium for the Imperium to be designated as TL15 overall, not to mention that corporations can build TL15 manufacturing on any planet. Who makes a dividend from all the procurement contracts for the Army? Why that would be the shareholders - who just happen to be Imperial nobility, the Emperor and their family, and a few megacorp CEOs...
***** oh no, so the shareholders make even more money...
Agreed on all points. This post is additional comments.
"There are also economic factors.
The Imperial tax base is incalculably vast.
The Imperial Army must arm millions of soldiers* – and also move them**, feed them, house them and keep them supplied
The logistics officer swipes the unit credit card, and the problem is solved. Adventure hook: The travellers and their ship are commandeered to transport troops and/or equipment.
There is only so much TL15 manufacturing in the Imperium.**** This would need to not only provide all the new weapons and equipment but also all the spares and supplies required to keep it working."*****
These are challenges, but they are nowhere close to insurmountable challenges.
Imperial military planners would make their logistical projections using centuries of data. The economists (probably noble-born) would prepare an economic development plan that would meet these requirements and brief the Emperor. The Emperor would task the sector dukes and the megacorps (noble-owned) to build the required profitable TL15 manufacturing capability that could support military production as a secondary function in peacetime, and as a primary function in wartime. The Emperor would command the Imperial bureaucracy to develop a taxation system to provide the required funding. This would be an ongoing process over the centuries of the Third Imperium's existence, and IMO the bureaucracy would be very good at it.
Adventure hook: More jobs for noble characters, with lead-ins to adventures.
The Imperium has been at TL15 for so long that stockpiled weapons and equipment would have been manufactured at TL15, as are older ships. Even the Kinunir was TL15. Even older TL14 equipment would still be effective. There would probably be one or more subsector military depots, keeping stockpiled equipment maintained in case of a major mobilization.
"High-technology systems require a lot of support, and that requires large numbers of technicians capable of understanding it*. An all-TL15 army would need to educate its maintenance personnel to that level, at enormous cost.**
Equipment and vehicles would be designed for ease of maintenance, as in replace the damaged part. Only depot-level maintenance would need to understand how a component actually works. Why would the cost be enormous? There would be plenty of TL15 training resources like expert systems, etc.. Imperial military planners would understand the need for trained maintenance personnel and be prepared to train new technicians in the event of a major war.
Something else is the lack of political considerations. The rl paradigm of governments maintaining small militaries in peacetime then expanding rapidly in wartime doesn't necessarily apply to the Third Imperium.
The Third Imperium is an absolute monarchy. It is totally unaccountable to anyone, least of all the citizenry it collects taxes from. There are no competing fiscal demands from elected officials, constituents, social welfare programs, or anything else. If the Emperor decides to spend uncountable fortunes on a massive army and navy during peacetime, he does it.
All the challenges quoted from the book can be overcome with long-term planning and determined political will. The only limitations are the physical resources of Imperium and the tax revenue the Imperial government is able to collect.