It seems that there is almost a consensus among players (well, the people that are still playing and posting) that the legacy paths for Antiquity are fine. However, the legacy paths for Exploration have been criticized at many points in the discussion. So, how would they become more interesting?
Culture
Collect 12 relics.
It's fine to have one path that focuses on great works imho, and one on religion as well. Yet, to me at least, it feels like this is too easy to fulfill. Some wonders help, and if you choose the belief that your own cities give a relic when converted, befriend a city state, and research the techs and civics that give relics, you are always set. It's welcome that you don't have to run around the map with 20 missionaries to create relics, but I think it is now too passive. I don't really have a good idea how to change that without making it tedious again. For example, saying that any conversion (regardless of first or later) creates a relic but you require 50 could be quite tedious. This could be a tiny bit more interesting if cities give more than towns, temples and wonders increase that, etc. But I don't think it would really improve the path. So, maybe this requires a new religious gameplay first.
Economic
Gain 30 points from treasure fleets.
As much as this is hated by some, I think that at the base this works well. The problem is the RNG of treasure resource spawning. This isn't that much an issue on smaller maps, but even there, the path's difficulty can reach from almost automatic (if you find 2-3 spots to conquer or settle early) to hardly possible (if no spots with more than 1 treasure exist). For an improvement, I would slightly increase the amount necessary but offer an alternative way to get points: trade. You need to have at least one settlement in the distant lands. Then, when you import a treasure resource from a DL civ, the nearest DL settlement of yours gains one treasure resource. This generates 1 additional point for the fleet, just as physical treasure resources do. While this still keeps the theme of going to the DL, it allows to focus on the homeland, with just creating 2-3 trading posts in the DL to trade for treasures. It will probably be difficult to get enough points just from that to complete the path – or at least, it should be difficult – it means that you can gain a few milestones without having to play each game in the same way.
Militaristic
Gain 12 Non Sufficit Orbis points. 1 point for each DL settlement, 2 if it was conquered or converted to your religion, 4 if both.
In general, I find this path is fine, but a bit too easy and one-dimensional. I'd keep the scoring as is but would add 1 point for conquered settlements in the HL, and 2 if it is following your religion. The required score should be higher, e.g., 16. That would translate to conquer and convert 8 settlements in the homeland, or 4 in the DL – with combinations between the two being possible. It's also possible to refine it more and make a distinction between cities and towns but I'm not sure if this complication would bring much benefit. Alternatively, it could be about population in the DL, and not simply settlements.
Scientific
Have 5 districts with 40+ yields.
This is currently the most boring path. It depends on science insofar as researching masteries gives bonuses to buildings. The problem is that you don't need too many of these, especially if you also generate culture to unlock policies and civics that increase yields (or wonders). Hence, almost any reasonable tile with 2 exploration age buildings or even antiquity unique districts can reach 40 yields. In consequence, you reach this legacy path's goal automatically as you go through the age and slot 2 specialists on the same tile. This path thus has two issues: boring and too easy. I'm not sure how to fix the boring part, but I think if it would just be harder, there is already something to be gained. If it were 50 yields per tile, you need tiles that actually have good adjacencies, and potentially research enough techs to get to 3 specialists per tile. But that still wouldn't be all that interesting. Yet, it would require some more planning and investment.
Culture
Collect 12 relics.
It's fine to have one path that focuses on great works imho, and one on religion as well. Yet, to me at least, it feels like this is too easy to fulfill. Some wonders help, and if you choose the belief that your own cities give a relic when converted, befriend a city state, and research the techs and civics that give relics, you are always set. It's welcome that you don't have to run around the map with 20 missionaries to create relics, but I think it is now too passive. I don't really have a good idea how to change that without making it tedious again. For example, saying that any conversion (regardless of first or later) creates a relic but you require 50 could be quite tedious. This could be a tiny bit more interesting if cities give more than towns, temples and wonders increase that, etc. But I don't think it would really improve the path. So, maybe this requires a new religious gameplay first.
Economic
Gain 30 points from treasure fleets.
As much as this is hated by some, I think that at the base this works well. The problem is the RNG of treasure resource spawning. This isn't that much an issue on smaller maps, but even there, the path's difficulty can reach from almost automatic (if you find 2-3 spots to conquer or settle early) to hardly possible (if no spots with more than 1 treasure exist). For an improvement, I would slightly increase the amount necessary but offer an alternative way to get points: trade. You need to have at least one settlement in the distant lands. Then, when you import a treasure resource from a DL civ, the nearest DL settlement of yours gains one treasure resource. This generates 1 additional point for the fleet, just as physical treasure resources do. While this still keeps the theme of going to the DL, it allows to focus on the homeland, with just creating 2-3 trading posts in the DL to trade for treasures. It will probably be difficult to get enough points just from that to complete the path – or at least, it should be difficult – it means that you can gain a few milestones without having to play each game in the same way.
Militaristic
Gain 12 Non Sufficit Orbis points. 1 point for each DL settlement, 2 if it was conquered or converted to your religion, 4 if both.
In general, I find this path is fine, but a bit too easy and one-dimensional. I'd keep the scoring as is but would add 1 point for conquered settlements in the HL, and 2 if it is following your religion. The required score should be higher, e.g., 16. That would translate to conquer and convert 8 settlements in the homeland, or 4 in the DL – with combinations between the two being possible. It's also possible to refine it more and make a distinction between cities and towns but I'm not sure if this complication would bring much benefit. Alternatively, it could be about population in the DL, and not simply settlements.
Scientific
Have 5 districts with 40+ yields.
This is currently the most boring path. It depends on science insofar as researching masteries gives bonuses to buildings. The problem is that you don't need too many of these, especially if you also generate culture to unlock policies and civics that increase yields (or wonders). Hence, almost any reasonable tile with 2 exploration age buildings or even antiquity unique districts can reach 40 yields. In consequence, you reach this legacy path's goal automatically as you go through the age and slot 2 specialists on the same tile. This path thus has two issues: boring and too easy. I'm not sure how to fix the boring part, but I think if it would just be harder, there is already something to be gained. If it were 50 yields per tile, you need tiles that actually have good adjacencies, and potentially research enough techs to get to 3 specialists per tile. But that still wouldn't be all that interesting. Yet, it would require some more planning and investment.