I have trouble wrapping my head around the type T Patrol Cruiser.
When it was created, it was the most powerful "small" starship available in the inventory. It had a decent balance of drive capabilities (it could catch anything but a few small craft) and was well suited to its paramilitary role of "customs inspections, piracy suppression, and normal safety patrols" as a peacekeeper ship.
In the
Grand Scheme of Things™ which includes later LBB5 BCS stuff ... the Type-T is basically a "low tech/low end militia" craft that is capable of pursuit and arrests in a law enforcement capacity, rather than any kind of "fleet on fleet" military naval combatant.
Why would you use a Patrol Cruiser instead of a System Defense Boat?
In a word ... Hegemony.
In slightly more words ... Hegemony and Influence.
You have to remember that Traveller becomes something of an "archipelago experience" at the interstellar scale (see:
Pocket Empires) in which some worlds are more powerful and have more influence (and/or technology) than their neighbors. This means that there is a market for security/law enforcement services in locations that cannot locally support those operations due to immature local economies (see: Non-industrial trade code) or a variety of other reasons.
One way for a specific world to increase its power (both hard and soft) is through exchanges ... of trade, diplomacy and military assistance. The Type-T is the TL=10 "answer" to that particular need for worlds capable of expanding their influence (and "protection") to neighboring star systems. By doing so, the sponsoring world gains "leverage" in a variety of spheres over their near neighbors ... because the Type-T is jump capable and can conduct patrol operations, meaning it can be deployed outside of the sponsoring home star system. This is a necessary building block on the way to an interstellar hegemony and the foundation for a nascent
Pocket Empire seeking to expand its sphere of influence.
In a TL=15 Third Imperium, the Type-T is a relic of a bygone age, now centuries past ... but still relevant to keeping the peace as a policing ship.
During a "
Long Night" type of era ... the Type-T could be "the most powerful ship in the sky" at any given time, simply due to a scarcity of competition!
Remember, Traveller spans a LOT of technological eras and ages ... sometimes, simultaneously!
It's a nice ship with a lot of weapons, but the Imperial Navy has better choices, I think.
A TL=15 Imperial Navy certainly does have better choices!
"I'll take 1 Tigress and keep the change. Thanks." 
But a TL=10 Planetary Navy, building for "local and near abroad" defense and security using domestic resources would find the Type-T to be a compelling option to expand their patrol range and security sharing arrangements with neighboring worlds.
In a universe that includes LBB5 or later, you're using Gazelles in place of the Type T Patrol Cruiser.
Gazelles are TL=14 ... while the Type-T is TL=10.
Gazelles are more of a "fleet recon" type of ship (more akin to a helicopter than a surface vessel, if comparing to wet navy missions and roles) that is capable of RAPID (self-)deployment when necessary to particular hotspots.
Type-Ts are more of a "beat cop" type of ship that just cruises around primarily as a deterrence to trouble, rather than as some kind of frontline combatant meant to take on all attackers and win every single time (without need for backup).
IMTU (that is, the one I'm using for my PbP and fanfic thingy) they're mostly used by the IISS for patrol/customs work.
Which makes a lot of sense.
Since so much of the IISS is standardized around TL=10 ... making supply chains MUCH shorter and easier to maintain ... the Type-T slots in rather nicely into the IISS inventory as either a "big scout" ship or as a "big courier" ship, along with a variety of other potential roles and missions.
In fact, now that I think about it, perhaps the S3 Scout Squadrons that showed up in the Fifth Frontier War tabletop game
were in fact simply Type-T squadrons!
This seems more law enforcement, than military.
THIS.
At lower tech levels (TL=10) the Type-T is perfectly adequate as a militia/military ship for a planetary navy.
At higher tech levels, the Type-T becomes something of a "hand me down" class to law enforcement and policing.
It's something like a coastguard ship.
As technologies advance, the Type-T gets relegated towards more civilian/peacekeeper roles, which it is perfectly capable of accomplishing relative to most free traders and small time merchant traffic (with the occasional pirate and smuggler thrown into the mix).
Perhaps not intended for the Imperial Navy, but it would certainly work for subsector or system navies.
Agreed.
For low tech "small time" planetary and subsector navies, the Type-T remains relevant to security, policing and pursuit or law breakers.
