In addition to the reasons already posted that rechargeable out perform Alkaline, another aspect is the performance curve.
When you install a set of Alkalines right out of the package, they may indeed put out more than 1.5 volts. However, the power begins to drop off almost immediately with use. As the charge drains the voltage drops, precipitously.
With NIMH that drop is far less of cliff,. and remains a flat voltage for some time and then voltage only really drops at the end of it's charge.
So not only do you get more than double the power/life of the battery, that power is at a good higher voltage for the entire life, and with less resistance for faster recycles.