The desktop version does not support a customer portal, so email (without using the “obsolete pdf”) is no longer functional.
Lubos has said he will add a solution such as emailing the invoice/payslip directly instead of attaching a pdf document containing the invoice/payslip. The functionality is also useful for those who want to send their documents directly to their clients rather than forcing them to goto their website to see the document.
Having an idea thread to record the idea makes some sense imo. Particularly as a related thread is locked Emailing of reports - #16 by lubos