Would I benefit from a headphone amp?

You need to upgrade your source..or get a portable amp. Maybe DIY?

WM-D6C has a decent headphone out and can drive almost all headphones.

I use a Yamamoto HA-02 with my D6C. Make sure you use the line out instead of the headphone output.

I find the HA-02 to be superior with my headphones than the headphone out of the WM-D6C.

Beats digital. Cassettes recorded on a well set up TOTL deck with a good well set up TT sound incredible on the Sony pro walkman.

Sure would...that's always the way to go

Cassette walkman? Is this a serious post? I was pretty sure they don't even make cassettes anymore.

I found that a dedicated headphone amp was a real eye opener using AKG 701s. This was a home based amp- OTL using 6080 NOS output tubes and one of my better 6SN7s as an input. It was not exactly cheap around $1500- But WOW what a difference. I refrain from suggesting the amp because the owner has been discredited, but his product if one of his good ones was amazing.

You would be better served by Sennheiser HD-25-II pros.

I think you would still be using the onboard headphone amp if you used an outboard amp to further increase the amplification of the headphones. Unless you have difficult headphones to drive, I don't feel this would be beneficial.

K