He was a Scott Boras client and Scott Boras client's almost always take the highest offer and he heavily advises them to do so. In a cap world that would be different. It would be like Panarin and the Rangers where he had similar offers from the Rangers, Islanders, and some other teams. Sure the Islanders was more but it was in the ballpark. Texas offer to ARod could have easily been 50M+ more (this doesn't say numbers others offered). In a cap world he would just get offered near the max from everyone (as happens in the NBA) and choose which team he likes best.
The reason baseball has so many different WS winners is because there is a huge amount of variance involved in the playoffs and legitimately anyone can win in a short series but you have some teams who have no chance at even getting there in the first place. This is also the case for the NHL which also has 13 SC champions the last 20 years (STL,WSH,PIT,CHI,LAK,BOS,DET,ANA,CAR,TB,NJ,COL,DAL). You would be better at looking at number of teams to make the playoffs or something like this since that is less prone to the randomness of winning a championship (obviously needing to account for differing number of playoff teams in each leagues).