The problem with a conversation like this is that, ultimately, it's all relative. One person's overpowered is another's easy mark. And all evidence is circumstantial and anecdotal; if I think Pyra's are easy prey, I'm unlikely to be convinced by someone else's argument. (and the other way 'round)
My circumstantial, anecdotal evidence is that the Pyra's popularity is because it's easy to understand. (note: not necessarily use, or use well) It's basically a big triangle you point at the enemy until it's dead. As a pilot, you're right up in front and can see where you're going (and thus what to point at); as a gunner, you can easily shoot at things right in front of you (which is great, since most rookie pilots don't always know about firing arcs yet); and as an engineer, four out of five major components are in easy reach (it's easy to figure out a path to follow when doing repairs). It's also great at ramming, which, to a rookie pilot who's always flying right at the enemy, will probably happen all the time. The ship is tough enough to take some punishment, and with a good engineer can stay flying for a long time.
It's not hard to see why a lot of newer pilots (and even experience ones) pick the Pyra in such great numbers. Yes, it's got its weaknesses — just like every other ship. But, as someone has already said, the vast majority of the game is played out in PuG matches by people who haven't flow together before. Do you want to spend 10 minutes explaining your Squid's fancy Minefield/Mercury/Flare strategy, or do you want to make things easier on your all-level one crew (and yourself) by taking the simple option?
The upshot of all this is that any kind of extra strength from the Pyra is unlikely to be fixed by a few damage tweaks or reducing some armor — what makes the ship attractive and 'easy' is baked into the very design. It's a matter of tactics, not numbers. Short of radically redesigning the entire layout of the ship (and thus destroying what makes it unique), any 'solution' is going to have to come from how people respond to the ship. If enough people learn how to counter the ship, the meta will shift and people will focus on a new 'overpowered' meta.