While, private messaging is now the current norm, with WhatsApp announcing in April about its employing end-to-end encryption by default for all users, making it virtually impossible for anyone to intercept private conversations.
Beta testers have disclosed that the preview version of Allo also features end-to-end encryption (using the Signal protocol) with unique identity keys for each individual users.
Albeit, Google disabled end-to-end encryption by default, and require users to switch to an “incognito mode” within the app, if they want end-to-end encryption via the Signal protocol.
As one possible side effects of the end-to-end encryption for conversations is that Google Assistant doesn't work in it.
Allo's incognito chats can have an expiry time just like Snapchat, with a small timer on top next to the recipient's name and photo, with a blue indicator for the expiration time.
Interestingly, Allo seems bit of a complicated take-on self-destructing message apps, but things are expected to change from the test preview versions and when the final release is out.