Paste a hostname. Tlsinspect opens a TLS connection, reads the certificate chain the server presents, and reports the expiry date, who issued it, every hostname the certificate covers, and whether the chain is complete.
A certificate can be valid and the site still break, because the server sends the leaf without its intermediate. Browsers on desktop paper over it from cache; mobile clients and API consumers do not. That failure is invisible to anyone looking only at the expiry date, and it is the one people lose a weekend to.
Whoever gets the call when the site stops loading. Someone who inherited a server, or runs three of them, and has no idea which certificate expires first. A developer debugging a mobile client that cannot connect while the desktop browser works fine.