I'm one of those Science Fiction types. While I love TOS/TAS, and I grew up with both on TV (TOS in reruns, TAS in first run)... the setting isn't 2D, at least not to me. The SFTM ships make sense, even the number of them, and the use of the term Starship by DCF and GR as a class name doesn't... if it had, the fanbase wouldn't have jumped on the constitution class. It's a throwaway in two episodes, and best explained as referring solely to the class, not the whole of the fleet. And the quote implies more classes in the fleet.
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.
I've generally looked at the numbers in the SFTM two ways: first, the SFTM provides a great feel for how things generally go in Star Fleet—the ratios between different ship classes, the jargon, the overall organization of operations—but in the end it's just a fun book to get the imagination going, and the numbers themselves shouldn't be taken too seriously. Either space isn't really that big, or the ships aren't really that few, or whatever. The stardates alone still confuse me. I've tried a dozen ways to tease out whether he was using a concrete formula to determine the ship production dates, and it still seems to make little sense beyond the basic 'use a number a little bit higher than the one before' formula of TNG.
Second, if we take the data in SFTM to be in fact wholly accurate, then we can assume that it just isn't showing the whole picture. If it is, then Star Fleet's self-image is greatly exaggerated. There would almost certainly have to be hundreds if not thousands, or even tens of thousands, of other ships in service, occupying a staggering variety of roles.
The ships in SFTM are described as 'Class I' vessels, so we assume that the huge fleets of Class II+ vessels are just ignored in the book—ships from previous generations, still in use because Star Fleet doesn't have the resources or time to scrap an old ship for a newer one. The dreadnoughts of yesterday might at best be classified as a destroyer in the Class I era, and anything of lesser formidability would likely be relegated to policing, patrol, training, or (probably most often) bulk transportation.
Also, we know of civilian space travel from the Mudd episodes. It could be the case that the vast majority of UFP space traffic is non-Star Fleet. In my imagination and games, I take both of these points to be the case. If you stick with only the 'civilian traffic' interpretation, then the UFP would be like a Federal government that employs a token military, which carries certain cultural prestige but has, in practical terms, no real power to act as a federal force.