I’d rather make a notice a <section> with a heading, or an <aside> if it’s not related to the surrounding content.
You could even add a more specific ARIA (or DPUB-ARIA) role like role="note", role="doc-pullquote", role="doc-tip", etc. But don’t use them unless you have multiple kinds of aside elements and need to help people skim.
Most of these roles actually map to the section superclass rather than the complementary role of aside, which isn’t always a problem: the aside element tells reader-mode implementations to remove the element, but the role tells assistive technologies more useful information. I use a similar hack for my in-page section permalinks.
If the notice is important to the surrounding content and reader-mode shouldn’t remove it, use a section.