Chelsea may have overpaid, I think a big part of that price tag had more to do with the marketing than what we've seen from him in the past year. While he's still the best American player and will continue to be for the foreseeable future, I think he was stalling out at Dortmund and a change of scenery was necessary.
This probably also puts him out of the reckoning for starts going forward for Dortmund, so he'll probably be itching to play all rounds of the Gold Cup. Historically, teams have been able to make six changes to the roster between the group stage and knockout rounds (US and Mexico have opted for younger and fringe players in the group stage, while bringing more top 11 guys in for the KO round). I'm not sure if they will continue this with the new format, not to mention the fact that it's a somewhat riskier strategy. Besides, it will also be the first matches of consequence for the USMNT in nearly 2 years. The GC would represent the next best opportunity for him to get back on track before the move but at the same time, he's missing the Chelsea camp.