Without the silliness about her intending to use the bond to compel Rand, let alone the stupid notion of proclaiming to the world the Dragon is her warder.

But I can definitely see Egwene in circumstances where Verin instructed Alanna to go in hiding and return to the Tower only once she was sure it was purged of the Shadow being very, very tempted to ask Alanna for the bond, if Alanna tells her it must be passed or dissolved, because Verin told her the Shadow knows about it and it's a big liability. Should it be dissolved, should it be passed secretely to someone else, Mother?

The bond would let Egwene know where Rand is, send him alarms to come to her, know at all times about Rand's health and if he's still alive, and it would prevent Rand striking at SG without her knowing. She would also have clues if he needs urgent help. Much advantages for an Egwene who still doesn't trust Rand (and whose trust in Elayne is shaken), and a much more attractive option than keeping Alanna at her side with everyone wondering why.

There's a nice twist to it too, because Egwene would more or less do what she blames Rand/the Asha'man to have done.