There is a comment in the source code that offers a little (but not much) more explanation:

# this code is broken and should never have been added.  i probably
# won't delete it, but it is definitely not up-to-date with respect to
# other features, and never will be.
#
# runtime role application is fundamentally broken.  if you really
# need it, write it yourself, but consider applying the roles before
# you create an instance.
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There are some obvious problems with run-time role application. For example, if you have an existing object $o, and you then apply this role to it at runtime:

package Example::Role {
  use Moose::Role;
  has thingy => (is => 'ro', isa => 'Str', required => 1);
}
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Then what is the value of $o->thingy? If you consider a role to be a contract that an object is obliged to implement, then the runtime application of Example::Role to $o is breaking that contract.

For runtime role application to an object, I'd use Moose::Util's ensure_all_roles function. It still suffers from the same problems but at least it doesn't have this annoying warning message. :-)

PS: the deprecation was committed by jrockway so if you need a definitive answer, ask him.