In the STS Authentication Protocol, why are the signatures encrypted?
The encryption of the signatures

$\;$ keeps the identity of the initiator (Alice) confidential, even against active attackers
$\;\;\;\;$ and
$\;$ keeps the identity of the responder (Bob) confidential against passive eavesdroppers
$\;\;\;\;$ and
$\;$ provides some protection against identity misbinding attacks,

$\;$ although not as much as a good protocol should have

.