I don't really understand how you can consider this a random plot-device power up. I assume you are talking about Cavendish, a character with quite a high bounty and whose strength had barely elaborated on, so I really don't get why you call that a random power up as even though it hadn't been shown yet, he already had that power since he was first introduced. Also Oda has been introducing countless of characters in block B, C and D and gave for several of them some background info. What he just did in block D is pretty much the same things he has been doing in the previous ones.
He isn't underestimating the Strawhats, he went even so far as using the WG to counter them. I mean people like Moria, Crocodile and Enel just plainly looked down upon them the Strawhats like they were a bunch of worms. Even though Doflamingo considers himself superior, he at least anticipated Law & Luffy and he was actually quite efficient in breaking the alliance. The problem for Doflamingo is that the situation escalated into something that was impossible to predict due to the amount of unexpected variables. I mean how was Doflamingo supposed to anticipate an admiral + a vice admiral, the Revolutionary Army, Big Mum, King Riku, Rebecca, Violet and the fairies? How was he supposed to know that Luffy had a supposedly deceased elder brother that appears to be in fact alive, is part of the RA and has the same feelings about Ace's fruit as him? How was he supposed to know that the fairies, who hadn't done anything since he took over the country and didn't even react when he kidnapped their kin, would use this exact moment to not only rebel, but join likewise into an alliance with the Strawhats and that they even had made a secret passage? How was he supposed to know that Bartolomeo is a fan of Luffy and would even protect Bellamy, who would then lead Luffy out of the Colosseum?
Doflamingo had anticipated the Luffy & Law alliance and anticipated their actions based on Luffy & Law's personalities and histories and he did quite a good job at that as Luffy took the bait and Law got beaten and captured, but how could he have anticipated all those situations and variables which had no visible connection with Luffy or originally didn't even had any connection at all and just happened as they went? As Mihawk said during the war: Luffy has the ability to rally everyone around him wherever he goes, but try to predict how something like that will unfold in practice.
The only part where Doflamingo seems to truly underestimate the Strawhats, is their individual combat ability as he seems pretty confident that they can't win from his family executives in one on one fights.