What does Pyroak's current movepool and typing combination imply it could do?
When I look at Pyroak's movepool, I'm blown away at the amount of pretty reasonable choices it has to run offensively oriented sets. Its two STABs, Fire and Grass, are absolutely incredible when paired together as they give Pyroak an answer to both Steel types and Water types, which would each give the individual types trouble. There are only a couple mons that are common in the current meta that resists both of these types (Heatran and Astrolotl for example) but even then Pyroak gets Ground Type coverage too. In fact, Pyroak's coverage, while occasionally redundant is absolutely absurd if you give it a good look. With access to both physical and special coverage for Ground, Steel and Dragon moves, Pyroak has the coverage to hit most common meta threats (save Venomicon) Of course, given these aren't STABs, they often will require some boosting, of which Pyroak ALSO gets. Maybe one of the most out of place boosting moves on Pyroak, Dragon Dance is present and could theoretically make Pyroak a serious threat to its foes. Furthermore, Pyroak gets White Smoke, which gives it some security in making its boost and not having to fear things like Intimidate from stopping a sweep. And there's also the possibility that Pyroak may get chipped, which may be somewhat of a problem if not for the fact that Pyroak also gets reliable recovery in Synthesis. It is of course worth noting that not every single move can be run on Pyroak, but it doesn't change the fact that Pyroak has a multitude of theoretical options. A Fire/Grass Pokemon with access to Ground coverage on both sides of the Physical/Special split, means of boosting both Attack and Speed with multiple different moves (Swords Dance, Dragon Dance, and Growth) + White Smoke security with those boosts, and self reliant recovery (Giga Drain and Synthesis) doesn't come around very often, and yet, Pyroak doesn't see much if any offensive use.
Presently, Pyroak's best spread is a physically defensive wall that sets up rocks, throws status around and waits to die. Pyroak has essentially no offensive presence and is often a big hurdle to new CAP players attempting to figure out what is a good attacking type against Fire/Grass (Flying, Poison, and Rock). Its stats leave much to be desired offensively, but posts an agreeable 120 / 105 / 90 bulk, which would be useful, if Fire/Grass weren't an awful defensive combination. As noted, some of the most common attacking types on CAP right now are moves that Pyroak is severely weak to, with especially strong users of moves like Brave Bird, Hurricane, Gunk Shot, and stone Edge being thoroughly present. Furthermore, Fire/Grass is a subpar defensive typing, offering resistances to only Grass, Electric, Fairy and Steel type moves, and a requirement to run Heavy-Duty Boots without taking 25% damage every switch-in. And it's a shame too, because Pyroak would absolutely benefit from having some form of general recovery through Leftovers + Leech Seed / Synthesis. Another issue Pyroak faces is the direct competition with Ferro thorn as a bulky grass type Pokemon. Ferrothorn does everything Pyroak wishes it could do, better. Pyroak isn't technically a water resistance because of its Fire Type whereas Ferrothorn gets extra resistances fromthe Steel type (which also grants Ferro an immunity to Toxic Spikes which Pyroak lacks). Pyroak doesn't have access to Spikes whereas Ferrothorn has both prominent entry Hazards. Hilariously Pyroak even has a lower Attack stat than Ferrothorn (70 vs. 94).
To sumamrize, Pyroak has a plethora of offensive options based on movepool and typing, and yet it can't use any of them given the defensive nature of its stats. Because of this imbalance between typing, mnovepool and stats, there is, quite frankly, essentially no competitive reason to run Pyroak in today's meta.
What is currently gatekeeping Pyroak from being successful in any given role? How do we mitigate said weakness(es)?
Pyroak is like trying to use a Phillip's head screwdriver to screw in a flat-head screw. It looks like it would work when you pick it out of the toolkit, but then you find that it's just thoroughly unfit for the job. I don't want to postulate too much on the rather flavor-based approach that was done to create Pyroak more than 10 years ago now, but I wish I were there to have told them that Pyroak's defensive stats and abilities directly conflict with Pyroak's offensively oriented typing movepool. It's a little incredible just how much Pyroak is competing with itself here given everything it has to work with. Pyroak's typing and moves want it to be a fast and hard hitting mon that dies fairly quickly, or a setup sweeper that can clean games later, while Pyroak's stats and abilities want to preserve its longevity and be able to survive a variety of hits from a Gen 4 metagame (especially Critical Hits I suppose). I am of the opinion that in order to "fix" Pyroak, we will need to do a couple of changes, like adjusting multiple aspects of its big four (typing, moves, ability, and stats), rather than a single major patch.
What roles could Pyroak feasibly fill in the CAP metagame?
Presently in the CAP metagame, the sole offensive grass type we see on teams outside of Hyper-Offense is Kartana. Rillaboom and Jumbao have fallen off for a while now and are unlikely to return anytime soon with the creation of Venomicon. Tapu Bulu occasionally sees use if only to provide teams with Dragon immunities and Grass Terrian Support while still hitting Flying Types, but this is only done on very specific teams. Necturna exists to an extent, but is really only ever used explicitly on Hyper Offense. The absence of commonplace offensive Grass type Pokemon likely stems from the fact that Flying type moves are extremely good (i.e. unresisted by most types), and many of the best mons in metagames both current and past resist Grass type moves (Heatran, Dragapult, Venomicon in the curernt meta, Tomohawk Astrolotl, and Jumbao is previous iterations of Gen 8, etc.) .
Pyroak absolutely has the potential to fill the niche of "Offensively oriented splashable threat" with proper adjustment. A Fire/Grass combination with the previously listed coverage moves provides Pyroak with plenty of options for filling a role as a boosting sweeper, a choiced attacker, or even an offensive utility presence similar to Astrolotl (with its main niche being it having a much more reliable answer to bulky Water types like Slowbro and Toxapex). While I will refrain from posting specific ways I think Pyroak can be fixed, I thinkthat leaning into an offensive Grass type threat is the way to go.