While a drummers job is to keep tempo, it's also their job to set the rhythmic FEEL, or groove.
A lone click has no heart, feel, or groove.
A drummer has to practice playing to click enough to be able to introduce a songs feel to the cold perfect timing of the click, while keeping that feel alive. Without that practice, a drummer tends to concentrate on the click too much and not only the timing varies, but the groove varies -- in all the wrong places.
I've worked with a drummer like this and I've found that it's actually a positive feature of his and I just have to alter the recording approach to fit him (With practice he has gotten much better with just a click). The reason it's positive because he can play absolutely brilliantly, groovy, and with great feel live. This is because his musical energy comes from playing with other people. He can very easily feel what everyone else is doing and where eveyone is going and compensate yet keep eveyone on track and in the groove. But he can't feel that non-human click.
So in recording with that particular drummer, I pick the key rhythm instrument (bass, guitar, keys) and play along with him in headphones while he is recording the drums. Get a good headphone mix with a strong click, the rhythm instrument, and drum bleed if needed, and he is good to go.
As a drumming practice, I suggest playing to just a click for 1/2 hour at a specific tempo. With no songs in mind! Just create beats to the chosen tempo until they groove. After making a beat groove for a few minutes change the beat. After a while it will be obvious how much of a tool the click can be. The coolest thing is that one can make 120 BPM feel fast, slow, laid back, rushed, funky, hyper, etc. while with all those feels being perfectly in time. When this is discovered the click becomes a friend.
Hope that helps...