Nimbostratus
Cirrostratus
Security: DNS is typically situated closer to the client. Some organizations prefer it to be on the perimeter, outside of the internal network. LTMs are generally installed near the servers behind a DMZ. Having a GTM-LTM combination unit forces a compromise in location.
Functional: There isn't a significant benefit to having GTM co-located with LTM. The traffic doesn't necessarily flow through the same LTM as the GTM which is responding to the client. Clients will always traverse the GTM and LTM modules separately. Whereas with ASM, APM, WAM, and maybe WOM, traffic would benefit from those modules being co-located and not having to traverse the "stack" multiple times on separate units.
If LTM and GTM are combined you're going to want to upgrade all of your GTM's together, which also means upgrading all of your LTM's. However if you've de-coupled LTM from GTM then you can run different LTM code versions in different DC's without running into versioning conflicts. This is a reasonably common practice especially when moving to a new major release. Upgrade one DC and let it run for a few days before upgrading the other(s). This way the rollback is to simply use GTMs to shift the traffic.
Adding GTM to an LTM unit also takes up a module slot that you may want to use later for a different module like ASM, WAM, etc.
Cost: Generally there are two LTMs per datacenter. You wouldn't want to have GTM licensed only on one unit in a redundant pair. So it would require four licenses of GTM, rather than two standalone GTM units.
Organizational: DNS is usually not maintained by the same team that deals with the applications. Sometimes it is easier to put GTM on its own device.
Aaron