Under certain circumstances, such as when utilizing multiple domains in a forest or having a trust between forests, you may not want to present your end-users with an opportunity to select a different domain to login to; the reason being, they may not have rights to login or it could cause confusion and questions to the help desk.
It is possible to disable the dropdown so that users do not have that option. The following Microsoft article describes how this is done.
The primary setback, however, is that if your users have to be trained to enter their FQDN login, sometimes referred to as their federated login, they may not like the new format.
normal login : userA
Federated login : userA@mydomain.com
If user credentials are not cleared at logoff, then the longer login name may not be as big of a hassel as it would only have to be entered once. Otherwise, there is likely to be some squawking at the new, longer login format.