Many of computer software now are generating "In-between" for animation, what do you think if you want to enhance timing for animation?

i have attended a session for one of Pixar animators before, they are animating characters frame by frame, they ar not using In-Between interpolation at all.

for sure you can start creating your keys using spline curves interpolation; then back your curve to frames to edit your animation frame by frame to enhance your animation timing and performance.

but is there anyone out there do it for all animation types? :)

It depends on what your goal is to archive. 

Yes, your correct most Softwares do have 'smooth' keyframe interpolation settings set by default - automatic in-betweens. This to give you basic eye pleasing movement as the software developers see it.  However, if your trying to block/plan Important Poses of a character/shapes movements to story script/audio dialogue then I would start animations by 'Steps or linear' keyframes firstly. (Most animation apps have F-curves editor) - change the curves to affect speed vs time. 

Then once happy and approved by senior animator then convert all your animation keyframes to 'Spline curves' to begin polishing and fine tuning. 

 With regards to Enhancing animation best thing is to research (real world behaviours for point of reference) ask yourself 'How fast does this subject move over time'. Look for their center of gravity in relation to body mechanics. Read on12 principles of animation by Disney animators examples - Keep Practicing...then exaggerate if you're producing cartoony style. 

Heavier items will naturally move slower vs lighter shapes, that's something you'd try tell your animation app. 

Animation as a whole is not the easiest thing to master unfortunately. BUT, Keep animating.....