You can use PowerShell to configure a customized per-site Anyone sharing link period for different sites. Public sites might have a 365 day period while more confidential sites might have a more restricted period. All it takes is the Set-SPOSite cmdlet to set the necessary properties and you have a customized policy.
SharePoint Online and OneDrive for Business support the ability to protected Anyone links with passwords. The idea is good and the feature works well, but some Office 365 tenants have problems with the idea of using Anyone links because, as the name implies, anyone who has the link can use it to open a document.