I feel that rebalancing Aristocrat Apollonius, and other legendary advisors (And more besides) needs to be done with utmost consideration. For instance, if you want to go Greek Calv, you currently have 2 options available to you - Aristocrat, as mentioned, but also Solon, who gives Hippokons +15% crit chance. Thus, if you want to build Hippokons, you go with Solon. Aristocrat is thus only the second option for Greeks when building Hippokons. However, as Prodromos don't have any Age 4 advisor that buffs them, you can go Aristocrat for Prodromos, making them slightly more beefy, perhaps able to survive 1 additional hit from some mobs, but also giving them yet another speed buff, allowing them to vroom along at 14 movement speed, essentially becoming the fastest unit in the game.
So, buffing Aristocrat to, say, +25% extra health and speed doesn't really change it's value in a Prodromos build, but it would push out Solon with a Hippokon build. As I see it, that's fairly undesirable, as it narrows the variety of builds you see in the game.
On the other hand, buffing Aristocrat to, instead, provide +15% health and speed to Prodomos, AND causing movement speed multipliers on a Prodomos to also affect their attack would not only make Aristocrat more desirable, but even change up the gear used on Prodromos - Instead of slapping some Gauntlets on him, you would instead want to use movement-speed boots in the soldier gear slot. You could even pick up Commander Cassivellaunous and Tribe Leader Andrasta in a Prodromos-focused build, which, in this situation, would increase Prodomos' movement speed to an amazing 17.9 movement speed, along with a combined 85% damage increase to Prodromos. You could even sacrifice some survival to go full movement speed, which would lead to 20.3 movement speed and an incredible 110% damage boost!
Probably too OP now that I think about it. Still, I feel this is the direction that Legendary advisors should go - They shouldn't completely smash already existing advisors for a particular build, but instead be for a new build, or an incredibly good alternative, like Bolt Carrier and Grand Engineer, or Coin Curator vs Tusk Sharpener