Difference between BIGIP-LTM and BIG-IP GTM

But sounds defeating the purpose, if all requests go to GTM1 and it is the GTM1's job to decide where to send the request, then anything going to DC2 will have extra delay equal to talking to GTM1 and then re-rooted to GTM2 ? It sounds better if there was a separate GTM who's job would be to load balance between two or more DCs without the need for a separate GTM in each DC, just a LTM in each DC.!!!! Am I wrong.???