I wonder if they did that so that they could stagger the development so that the largest potential revenue driving (and larger fan supported) of those sports do no lose any home seasons. If they were to keep each sport in their current location, then every sport would have to lose at least one home season while their new stadium was being built. Basically, by moving each team, they can ensure that Soccer and Baseball are not impacted. For instance, it would look something like:
2018 : NEW SOCCER STADIUM CONSTRUCTION -- Soccer plays at Old Field, Baseball plays at Old Field, Softball finds alternative home
2019 : NEW BASEBALL STADIUM CONSTRUCTION -- Soccer plays at New Field, Baseball plays at Old Field, Softball finds alternative home
2020 : NEW SOFTBALL STADIUM CONSTRUCTION -- Soccer plays at New Field, Baseball plays at New Field, Softball finds alternative home
2021 : ALL COMPLETE -- everyone is new home
Or I guess the other option would be to, instead of having the Softball team have to find some random home (probably not a great location) for 3 seasons, maybe they have the Baseball team be the one who loses their home for a few seasons and they get to play all home games in Hartford at the new Dunkin Donuts Stadium?