I tend to agree. If the Dragoons lost, its because they took on vasty more powerful opponents. Anton was a significant under dog, and the Dragoons were nearly enough to tip the ballance in his favor (had he not pushed his golden geese too hard, he might have very well won).
Unlikely, since he was used as a dupe by other powers hoping to maximise the chaos in the Free Worlds League for their own advantage. The majority of the League's military was staying uninvolved thanks to the Home Defence Act, so it's not as though the FWLM was going to drop on them in force.
The 4th Succession War pitted a damaged Dragoons (post Misery) against a very large part of the Draconis Combine, one of the historicaly most millitarialy capable Successor States.
Historically being the key word, there. The Draconis Combine has constantly been on the back foot since the Second Succession War, and kept getting hammered by the Federated Suns and Lyran Commonwealth during the Third and Fourth Succession Wars, the War of 3039, and beyond. The DCMS was headed by a man who had suffered a stroke that impaired his decision-making and leadership ability, and Hanse made use of his inability to focus on anything other than Jaime Wolf at that time to make them the bait of a well-laid trap. They still took so many casualties after Misery and the Fourth Succession War that they needed decades to rebuild.
Elson's was a civil war, so the best fought the best.
Costing the Dragoons their then-leader, many troops, and resulting in a hiring ban being placed on them for (IIRC) half a decade.
Outreach and Mars were against the Word of Blake, a secret super power that was able to take on all five Successor States at once and sow significant chaos and do considerable damage; the much larger Case White was an even worse falure than the Dragoon's assualt, and Stone's final assualt on Terra with more power even than Case While still took a significant beating.
The much larger Case White took place some years later, after heavy build-up from the Word of Blake, and with ComStar ROM pretty much all being secretly Word of Blake ROM agents. The Dragoons' strike came as something of a surprise and essentially spelled the end of the Dragoons as a combat force for the remainder of the Jihad.
Then there's the matter of their Battle of Hesperus, when the Eridani Light Horse, a smaller force, beat them back.
That the Dragoons are the best isn't really in question, I don't think. Everyone takes their lumps. If you're Jacob's Juggernaughts, you take it from the Capellans that you and your allies just sprung a great ambush on (oops). If you're the Dragoons, you take it from a whole nation-state, and come back to do it all over again.
That they are the best mercenaries is not really important; someone has to have that title, and the Dragoons didn't bear that mantle for as long as others like the Northwind Highlanders, 21st Centauri Lancers, or Blue Star Irregulars did given the amount of time they had to keep taking out to rebuild.
The Dragoons really didn't recieve the kind of hyperbolic fiat they are constantly accused of getting. Other factions recieved far, far more (hello, CapCon...) and they fly completely under the radar despite being major players in the storyline.