Most navies would like input into the type of "hull" they want to operate. Things like tempo of operations have to be considered. In small navies especially, ships have to spend a lot more time "at space" or on operations than the equivalent merchant hull. The navy a hull is being built for will want to know the vessel can stand up to the type of punishment they expect it to be subject to.
I can see lots of merchant standard fittings being built into smaller warships and auxiliary vessels but would an off the shelf merchant ship stand up to the kind of use a naval crew will give it? Will conversion give you a warship or escort that has had all the weak spots and blind spots designed out?
And finally there's the matter of pride. The ships of your navy are the representation of your nation far and wide. If you start defending your space, escorting your convoys and chasing down pirates in a converted merchant ship are the neighbors going to start calling you Ferengi?

They might start to suspect your economy isn't so good or that your tech base is substandard and that effects the economy.
Build a real warship and make a statement
I don't think Traveller rules capture such things as tempo of operations or blind spots, and it's not clear that such issues as applied to modern ocean-going ships would apply also to far-future spacecraft capable of interstellar flight. Per Striker/High Guard/MegaTraveller, ANY Traveller ship hull is about as strong as the armor of a WW-II T-34 tank, the result of the need to resist micrometeor impact and the odd solar flare.
No, a converted merchantman will not stand up to the kind of use a naval crew would put it to. However, merchantmen are likely to be drafted into military roles for the same reason they've always been drafted into military roles: 1) it's cheaper, 2) it's faster, 3) current circumstances make cheaper and faster a high priority.
http://uboat.net/allies/warships/ship/3326.html
"On 25 August 1939 the passenger ship Jervis Bay of the Aberdeen & Commonwealth Line Ltd, London was requisitioned by the Admiralty and converted to an armed merchant cruiser. Conversion was completed on 15 October 1939.
"Displacement: 14164 BRT
"Armament: 8x 152mm, 2x 76mm
"Speed: 15 knots
"Career:
"October 39 - April 40: South Atlantic Station
"May 40: Bermuda Convoy Escort Force
"June 40 - November 40: Bermuda and Halifax Escort Force
"On 5 November 1940, HMS Jervis Bay (A/Capt. Edward Stephen Fogarty Fegen, RN) was shelled and sunk in position 52º41'N, 32º17'W by the German pocket-battleship Admiral Scheer while engaging the superior enemy ship in a heroic, if hopeless, fight to give the 37 merchants in the convoy HX-84 a chance to escape, because the armed merchant cruiser was the sole escort. Her sacrifice allowed many ships of the convoy to scatter and escape in the night. Capt. E.S.F. Fegen (RN) was posthumously awarded the Victoria Cross."
The Royal Navy modified 54 merchantmen as armed merchant cruisers during WW-II. Typically they were given 6 to 8 8" guns and some smaller guns. They were used as convoy escorts and troop carriers, and they were made for a simple reason: the Brits needed armed ships for escort to counter German surface raiders, they needed them ASAP, and it was faster and cheaper to slap guns on something already afloat than to build something from scratch. 15 were lost during the war, most to submarines, though two were lost to surface warships and one to a German armed merchantman:
HMS Jervis Bay fought a heroic battle against German battleship Admiral Scheer, getting sunk but stalling the battleship long enough for most of the convoy to get away.
HMS Rawalpindi, another armed merchantman, was patrolling when she encountered and was sunk by German Battlecruisers Scharnhorst and Gneisenau while the pair were attempting to slip past Iceland into the Atlantic; the encounter forced Scharnhorst to retreat to Germany to avoid British searchers.
HMS Voltaire was patrolling in the Atlantic and encountered Thor, a German auxiliary cruiser. Thor itself was a freighter that had been armed and converted for war, in this case for commerce raiding. The two traded shots, Thor came out on top. Thor had previously tangled with British armed merchantmen Alcantra and Carnarvon Castle in separate engagements, the battles ending with neither combatant sinking the other.
A noteworthy German converted merchantman was Kormoran, which managed to sink an Aussie light cruiser, HMAS Sydney. However, Kormoran (like most other German converted merchantmen) was designed for stealth, its weapons designed to be raised from within the ship by hydraulics or hidden behind panels. It's stealth advantage played a big role, but Kormoran was still crippled in the engagement and had to be abandoned and scuttled by her crew.*
As I mentioned above, the merchantman is no substitute for a purpose-built warship. Something as basic as a missile bay or a wee bit of armor can give the DE a big advantage over an equal weight of auxiliaries. However, the merchantman auxiliary can serve well in certain circumstances. Just as you can field more Destroyer Escorts than Light Cruisers, you can field more auxiliaries than Destroyer Escorts. Modified Fats against a Chrysanthemum plays out rather like the Jervis Bay vs Admiral Scheer engagement, but they also serve well in the role Thor played - as commerce raiders - and they can defend well against such commerce raiders. So, a balanced force would probably include cruisers, DEs,
and auxiliaries as the strategic picture warranted.
*Not clear whether this exchange could play out in a Traveller far future, since the time it takes for the auxiliary to raise turrets, lock on, launch missiles, and then have missiles travel from auxiliary to target would be plenty for the target DE to throw on full agility and defenses. Beams might work, but they don't have as much punch and therefore might not dish out enough damage in that critical first shot to give the battle to the auxiliary.