How might it benefit an organism to have the nucleus near the centre of its cells?

Truly, it benefits since it makes it simpler for the waves to control everything in the cell and for the cell to work all the more appropriate and snappier. 
Just the cells of cutting edge organisms, known as eukaryotes, have a core. For the most part, there is just a single core for every cell, except there are special cases, for example, the cells of ooze molds and the Siphonales gathering of green growth. More straightforward one-celled organisms, similar to the microbes and cyanobacteria, don't have a core.

Ihaven't done that yet, so no idea,but this is not the right place to ask

There would be one bar shorter than the bar for peaches.