As for changing PowerPlay altogether, I'd make it such that players pledge allegiance to one faction of their choosing. That allegiance then determines the advantages and disadvantages they face across the galaxy. I'd allow for upwards of 33 PowerPlay characters, each championing their own government and allegiance, following the allowed combinations of allegiances and government types.
| Alliance | Empire | Federation | Independent |
| Anarchy | y | y | y | y |
| Communism | y | | | y |
| Confederacy | y | | y | y |
| Cooperative | y | | y | y |
| Corporate | y | y | y | y |
| Democracy | y | | y | y |
| Dictatorship | y | y | | y |
| Feudal | y | y | | y |
| Patronage | y | y | | y |
| Prison Colony | | y | | y |
| Theocracy | y | | y | y |
Let's say for the sake of argument that I'm pledged to an Alliance Corporate faction called Alliance Office of Statistics (the player made faction I helped create).
When dealing with that faction (in whatever way), I get a 20% bonus (or 20% discount where applicable, but such that I can't just buy and sell stuff at the same station and make money out of thin air).
Since it's an Alliance faction, when I deal with any Alliance faction, I get a 10% bonus. Reputation defaults to Friendly.
Since it's a corporate faction, when I deal with any corporate factions, I get a 5% bonus. Reputation defaults to Cordial.
These stack, so if I'm dealing with other Alliance corporate factions, I get a 15% bonus. Reputation defaults to Allied.
If I deal with Empire or Federation factions, I face a small penalty of 5%. Reputation default to unfriendly. This stacks with the government type bonus, cancelling it out to 0% and neutral reputation).
If I deal with government types that are hostile to mine (Corporate and Communism I would suspect), I face a 10% penalty. This also stacks, so one could end up with a 15% penalty, in which case the reputation would default to hostile.
Bonuses can be adjusted to make more polarizing things of course.
If a PowerPlay champion is the highest ranked in his allegiance, their followers gets bonus A.
If a PowerPlay champion is the highest ranked in his government type, their followers gets bonus B.
PowerPlay champions ranked 1, 2 and 3 overall, give their followers get bonus C (at varying levels).
Now, this suggestion does mean that some characters need to be remade to champion just one government type supported by their major allegiance.
E.g. ALD and Patreus need to figure out who gets Feudal and who gets Patronage, Torval would likely end up with Dictatorships and Aisling Corporate (makes more sense than Anarchy and Prison Colony). Hudson would need to change as well, and the most reasonable outcome there is Confederacy. Yuri Grom would likely end up with independent Dictatorships, Antal with Communist and Archon with Anarchies. These are just guesses based on their current ethos and established information.
This kind of change could/would give everyone a stake in the galaxy's political makeup, and it'd result in some interesting situations. Li Yong-Rui and Mahon are both Corporate champions, so they'd be rather natural allies, but Winters would be a more obvious choice for cooperation than Hudson, and it would make for interesting inter-allegiance conflicts. For example, it might make more sense for Winters commanders to fight for an independent corporate faction than for a Federation democracy in order to give her a leg up on the scoring chart.
Speaking of scoring. This becomes far easier than the current mess where no one really understands how to calculate it.
A champion gets 15 points for each controlled system (e.g. Alliance Corporate in control), 10 points for each allegiance controlled system (e.g. Alliance) and 5 points for each government controlled system (e.g. Corporate). Additionally they get 3, 2 and 1 point for controlled assets following the same rules. That means a system is worth a minimum of 18 points to someone (15 for the system, 3 for the controlling asset). By having assets affect the score, all conflicts have values, not just the ones for control.
I'll add in a table with scores for the current characters based on eddb data, once I manage to complete the query.
Edit:
Scores are based on some relatively old data - specifically this particular distribution:
| Alliance | Empire | Federation | Independent |
| Anarchy | 28 | 1 | 2 | 1414 |
| Communism | 17 | 0 | 0 | 376 |
| Confederacy | 7 | 1 | 1063 | 342 |
| Cooperative | 36 | 0 | 1 | 476 |
| Corporate | 121 | 2050 | 2742 | 1844 |
| Democracy | 80 | 0 | 2554 | 890 |
| Dictatorship | 30 | 899 | 6 | 748 |
| Feudal | 28 | 239 | 1 | 518 |
| Patronage | 70 | 2110 | 1 | 245 |
| Prison Colony | 0 | 38 | 0 | 108 |
| Theocracy | 1 | 1 | 2 | 84 |
I'm assuming ALD gets Patronage and Patreus gets Feudal for these scores
And with these numbers, this becomes the new PowerPlay results:
| Complete | Allegiance | Government | Score |
| Winters | 2,742 | 6,372 | 6,757 | 138,635 |
| Li Yong-Rui | 1,844 | 7,045 | 6,757 | 131,895 |
| Aisling | 2,050 | 5,339 | 6,757 | 117,925 |
| Archon | 1,414 | 7,045 | 1,445 | 98,885 |
| ALD | 2,110 | 5,339 | 2,426 | 97,170 |
| Grom | 748 | 7,045 | 1,683 | 90,085 |
| Hudson | 1,063 | 6,372 | 1,413 | 86,730 |
| Antal | 376 | 7,045 | 393 | 78,055 |
| Torval | 899 | 5,339 | 1,683 | 75,290 |
| Patreus | 239 | 5,339 | 786 | 60,905 |
| Mahon | 121 | 418 | 6,757 | 39,780 |
Now, there are a few things that really stand out here.
One - Mahon is dead last. This is because the Alliance is absolutely tiny compared to the other allegiances, with 418 systems while the Empire (the 2nd smallest) is 5,339. This means that collapse needs to disappear, as otherwise the Alliance would always be at constant threat of collapse, which makes no sense.
Second - one could argue that independents shouldn't get a massive bonus from their allegiances. They're independent, so it's not like an independent Democracy can call for help from an Independent Confederacy. If we do away with the allegiance score for independents, we get this result instead:
| Complete | Allegiance | Government | Score |
| Winters | 2,742 | 6,372 | 6,757 | 138,635 |
| Aisling | 2,050 | 5,339 | 6,757 | 117,925 |
| ALD | 2,110 | 5,339 | 2,426 | 97,170 |
| Hudson | 1,063 | 6,372 | 1,413 | 86,730 |
| Torval | 899 | 5,339 | 1,683 | 75,290 |
| Li Yong-Rui | 1,844 | | 6,757 | 61,445 |
| Patreus | 239 | 5,339 | 786 | 60,905 |
| Mahon | 121 | 418 | 6,757 | 39,780 |
| Archon | 1,414 | | 1,445 | 28,435 |
| Grom | 748 | | 1,683 | 19,635 |
| Antal | 376 | | 393 | 7,605 |
This makes the independent powers drop like a rock, as they are suddenly out 70,450 points, and as a result Li Yong-Rui is now the only independent power not in the bottom three. This doesn't change the fact that threat of collapse due to being in the bottom three would need to go away.
Collapse altogether, really, unless the player made factions that are pledged to a character wants to challenge them, at which point you could run some CGs to see if they can manage to overthrow them. This would also allow player factions without a PowerPlay rep to compete for a spot, but competing doesn't guarantee a spot. A Federation Democracy would (with the suggested scoring system) instantly occupy the 2nd spot, and there's no guarantee that the existing powers like the idea of losing some of their bonuses.