It occurs to me that while I've spent a fair bit of time talking about what I would like to see in improved Companions, I haven't discussed why I want to see these changes. So I'll do that now to provide some context for my thought process.
Observe the current situation with Companions. When going into a serious battle, you often see a very similar assortment of choices for who is brought in to help our Pirate. Swashbucklers pick choices like Fan Flanders and Contessa Argento because it fits their playstyle. Musketeers prefer fellow musketeers like Chantal and Bonnie Anne other other options like Louis le Bisque. Peter Quint is a Buccaneer's best friend, Privateers love Emmet, and Old Scratch is essentially all-powerful. Each class has a rather particular choice of who to bring, with little in the way of variation or experimentation.
This is because there is currently something of a tight limitation to what defines a good Companion. Chain Epics like Mojo Echo and Double Tap are ideal in order to dish out meaningful and consistent damage. Powers that provide good support or deal meaningful damage compliment the former nicely. The more Epic Talents you have access to, the better you are. Anything that doesn't match these criteria, from Ratbeard to Monkey King, is seen as a pointless endeavor. If a Companion has this potential, but is outclassed by someone else, it is seen as niche. There is little in the way of customization or variation.
What I want to see is a change to this status quo. By improving Companions that have currently fallen behind, the idea is that new options will become available. With new options there are more choices, and when there are more choices there will follow more playstyles. And if anyone says there are already plenty of playstyles out there, there are... for our Pirate. The Companions that follow our Pirate do not have the luxury of being able to equip different kinds of items to change themselves, and though their Epic Talents can be customized the above criteria for a good Companion somewhat limits their options. And so those criteria must be loosened by an influx of new options.
Here are a few thoughts on how this could be brought about:
Theoretically, Companions can be good without access to Relentless or Burst Fire. We see examples of this in certain builds of our good friend El Toro, and I remember the days when Shiruku Neko was a common choice. This kind of Companion could see more use, but only if they get what they need; a way to stand out. El Toro does this with his access to Espirit de Corps, and Barnabus sees occasional use due to his impressive offensive Powers. But you never see the likes of Monkey King used, and that is because he lacks these options. When designing Promotions or improvements for lesser-used Companions like this, consider giving them useful or uncommon Powers to make up for their lack of chain Epics.
Old Scratch needs to be taken down a peg or two. His current abilities, specifically his Mojo Flow series of powers, allow him to warp the metagame around his capabilities. He's pretty much the sole reason why Blood Flames are so popular, or why Gracie Conrad sees any use (if we're being honest with ourselves here). Old Scratch should not have the ability to make Powers do thousands of damage at once, and requires adjustment. I would suggest letting him only have one Mojo flow power, and reducing the boost from "Flow, Mojo, Flow!" to 75%. Be aware of the dramatic changes this may cause should it happen, though.
Epic Talents are key! If a Companion doesn't have selection available to it, it won't be able to express variation or have the same level of power as current top-tier Companion. In lower-level Worlds, this is brought about through Promotions to ensure Companions remain meaningful through story progression. In higher-level Worlds (from late Cool Ranch onwards) a large number of Promotions is unfeasible. So Companions obtained here must instead have a number of Epic Talents already at their disposal, from the moment they recruit (I call these "innate" Epic Talents). These Epic Talents will give them the skill they need to be considered by players.
I have a number of ideas for individual Companions as well, which I'll probably discuss in separate posts here. I just wanted to share a bit of my thought process.