I think heatmap outputs of architectures like CenterNet, OpenPose, etc. can be changed to coordinator outputs, and loss functions like focal loss can be modified so they can deal with coordinators instead of heatmaps. Is there any particular reasons that researchers use heatmaps instead of coordinators?
Why do popular object detecting models output heatmaps instead of coordinators of object directly?
To have a more powerful representational output. You can derive a bounding box from heatmap but not vice-versa. Also, in case of dense object detection it is hard to create bounding boxes for each object (people standing in front of each other).
That being the case, it is better to run a segmentation loss for these networks. It also leads to less confusion for the network. Also, it is a single shot creation of output. On the other hand, the bounding box approach will have the creation of a lot of bounding boxes then finding their objectness score and finally applying NMS (non-max suppression).
In regards to focal loss and use of bounding boxes, it is something that is a consequence of the heatmaps/activations that neural networks learns. They are built upon that and then regressed.