To answer the question: yes, a cooler can be too big. Why? Transmission are designed to perform optimally when the transmission is within a specific operating temperature range.
The range is pretty wide usually even on Linear Solenoid, Clutch Volume Learning/Adaptive units....Ford & GM 6/8/10 speeds, ZF 6HP & 8HP, Aisin 6 & 8 speeds etc.
150°F to 200°F is good target for most automatic transmissions.