First - Depending what you fly legislation limits us to 8,000 fpm.
Second - In deference to BOAC, if you can climb at a good rate to 'get in' a decent tailwind then there may be
possible savings on time and fuel. Of course, the opposite is true of a headwind.
Third - What BOAC said. Although a second caveat is that 'expedited' climbs (and descents) can be used to avoid potential collisions with infinite gain!