I still, at times, use handheld meters.
Part of that is that I still use some film.
When I am intentionally out to do landscapes, I have a Pentax Spotmeter along. My bag carries a D200, a TLR (for B&W), & an F2a (Velvia).
I have started using the spotmeter with the D200 (set to manual), more.
I can, with the camera on a tripod, the scene composed, check where I want to put tonalities etc. in the picture, without moving the camera around. I like doing it that way.
I find the D200's matrix metering to be excellent. But as an "old slide & zone shooter" the more deliberate approach is still useful, to me. Also, in switching between the medium format TLR, and the D200, it "fits" in the flow.
I rarely, but on occasion, use an incident meter with my walk-around DSLR, if I also am carrying a film body (and hence, have the meter along). For my shooting style, it can be handy in weird light.
I think, that if shooting digitally, and outside of the question of flash meters; whether or not you use a handheld meter depends upon, your subject matter, whether or not you "previsualize" through the whole PP when you are shooting, etc.
For me it is nice to use when I can. For others, with different styles, it would be a waste of time and an unnecessary expense.