If we accept the Technical Manual as 'canon' for RPGing in this era, don't we know EXACTLY how many and what kind of ships there are? There's a list?!
That list is HUGE. These are the numbers added at each appropriation.
Noting that ALL the ships with name lists show the initial NCC, with a few "heritage" exceptions.
20× Mk X DN as of SD 6066. (NCC-21xx)
14× Mk IX CAs as of SD_0965 (1× 10xx, 1017; 1×13xx, 1371 ; rest 17xx, 1701)
16× Mk IXa CA's as of SD 3220, plus 4 Mk IXa replacements for lost Mk IX in 4444 (NCC-17xx, 1712-1731)
111× Mk IXb CA's in SD 5930 (NCC-17xx & 18xx; 1732-1841)
20× Mk VIII DD's as of 0965 (NCC-5xx, 500-519)
10× Mk VIIIa DD's as of 3030 (NCC-5xx, 520-529)
26× Mk VIIIa DD's as of 4699 (NCC-5xx, 530-555)
15× Mk VII SC's as of 0965 (NCC-5xx & NCC-6xx, 585-600 - but no 587)
16× Mk VIIa SC's as of 3669 (NCC-6xx, 601-616)
9× Mk VIIb SC's as of 5099 (NCC-6xx, 617-625)
15× Mk VI TG as of SD 0965 (NCC-38xx, 3801–3815)
15× Mk VIa TG as of SD 3640 (NCC-38xx, 3816-3830)
110× Mk VIb TG as of SD 4990 (NCC-38xx & 39xx, 3830-3940)
?? Mk V Cargo Pods (NCC-50xx)
?? Mk IV Starliner Pods (NCC-40xx)
?? Mk III Refer Pods (NCC-30xx)
?? Mk II Dry Bulk pods (NCC-20xx)
?? Mk I Liquids Pods (NCC-10xx)
Aside from the HUGE buildup in 5930 and 4990...
There are issues also with sequencing.
The liquids pods potentially overlap the cruisers. Unless the prior cruisers were NCC's 1060+ and the pods numbered less than 60.
Likewise, the Dry Bulk are limited to 100 thanks to the DN's.
The gaps in the cruisers imply two prior cruiser allocations.
The SFTM is dated SD 7306.
Aside from the allocations looking almost nothing like actual authorizations for naval ships (they look more like aircraft allocations, rather than ships), the lack of losses for ANY non-cruisers, and the issue of the NCC- sequences, there's also a lot missing from the needed fleet, and it's top-heavy as hell.
In 0965, we have CA×14+DD×20+SC×15+TG×15, for 64 ships. If we assume a 95% on-patrol, and a 7 parsec radius (as noted in the SFTM for the core of the Federation), and only the surface of that sphere patrolled... that's an area of 615.5 square parsecs, and under 1 ship per 10 square parsecs. If we assume instead the volume... 1436.75 cubic parsecs... thats just shy of 25 cubic parsecs per ship. And that's JUST the core. As we know, the CA's left the core.
The implication being that 20×DD are adequate to patrol 1400 Cubic Parsecs. Thus we come to a sensor range of around 4.2 Pc assuming 100% coverage - the scouts are barely adequate for patrol duties, but would bring that range to 3.6 Pc.
Just that 7 Pc radius. The huge fleet buildup looks to be a "fill the exploratory zone"... But we know that it's not a sphere filled by the whole fleet, and the tugs imply large amounts of settlement - almost 1/3 of hte fleet.
The designs are good; the numbers not so much.