In practice, most businesses are simply handling this on a case-by-case basis since COVID is a temporary problem. Most home networks can handle the extra load as long as the employee makes sure that other latency-sensitive traffic, like gaming or video streaming, is kept to a minimum during the hours when they need to talk. If some home routers develop problems, IT staff simply build a queue and handle those one at a time. Sometimes they'll be able to access the router remotely with the employee's permission, sometimes they'll have to walk that employee through configuration steps to fix the problem. Sometimes the employee will just have to live with it unless the company springs for a new router or a higher bandwidth tier from the employee's ISP.
Business Phone Systems often come with feature codes you can dial to complete a task. This includes listening to and managing voicemail.

The last thing you want your potential clients to hear is stuttering simply because you weren’t able to prepare well enough for your message.
It isn’t always convenient to keep a browser window open that displays your online voicemail manager. Let’s face it, we probably have too many tabs open already.