I still use a handheld meter in the studio and outdoors, and I fear I am now a member of a shrinking minority. Certainly, in the age of digital capture, many well-regarded photographers have forsaken their meters, relegating them to the same drawer as their Polaroid backs, color-balancing filters, and film loops. I've seen forum threads where everyone advocated the chimp-and-check approach, with nary a whisper in favor of a meter.
No doubt, my reluctance to move on is partly historic. In the days of film, I usually had to shoot without Polaroid test prints or transparency clip tests, so sound meter readings were the only way to ensure that the previsualized image would be realized in the resulting transparency. However, for me, there is more to it. It's about speed, control, and professionalism. With a meter I can take a single reading of each light and make the appropriate adjustments to power and/or distance to get the lighting where I need it. Why would I want to use the less precise camera display in a multi-pass process to achieve the same end? And, if I'm chimping and tweaking with the customer present, how does that impact their perception of my competence and professionalism?
Look, if you don't already have a meter and you are just doing stuff for fun, or you work in a studio where the lighting is mostly locked down, then chimping may be all you'll need. However, if you work in challenging mixed lighting, take your studio gear on location, or work with rental gear in a rental space, you may find a meter a blessing.
This is my perspective. It may change. You are welcome to add yours in the comments.