[Rwp] Recording methods used for professional albums, need advice

[Jes]

Hi list.

So, I am in the process of recording an album of solo piano music into 
Reaper. Is it a good idea to record each part of a song separately? I 
don't mean the lead and the accompaniment tracks separately, that's a 
no brainer. I mean, record one phrase, then pause, record another 
phrase of a measure, then pause, etc? This way fewer mistakes are made 
in the recording process, and I have time to think about what I am 
going to play before I play it.
Then I can separate each section into items, place them appropriately 
on the timeline, and get tracks done a lot faster.
Is this method recommended? Does anyone else on the list use this approach?
Jes