Even though not technically required, is posting the Bank's Privacy Notice/Policy on its website a recommended practice?

Absolutely. See 1016.4(e)(2)(iii)

(iii) No substantial delay of customer's transaction. Providing notice not later than when you establish a customer relationship would not substantially delay the customer's transaction when the relationship is initiated in person at your office or through other means by which the customer may view the notice, such as on a Web site.

1016.7(a)(2)(ii)(C)

(C) Provide an electronic means to opt out, such as a form that can be sent via electronic mail or a process at your Web site, if the consumer agrees to the electronic delivery of information; or

1016.9(c) and (e) are also helpful, https://www.bankersonline.com/regulations/12-1016-009