You can't change this. Simple solution:
Don't shut down your phone any more (except when it runs out of battery).
If you switch off your screen only, your phone will go to sleep and won't consume much power. If it still eats too much battery, consider disabling wifi, background data, sync or even switching to airplane mode.
As noted in the comments the logo is only shown to beautify the startup of your phone and to not show you ugly boot messages as some linux systems earlier did and still do. Showing a complex animation does require some computing power but won't delay the startup very much.