Why use a Thinner Water Pipe to Branch off From a Tee
You are correct about the electricity analogy, the reasons are normally cost and ease of installation its easier, quicker and cheaper to install a 1/2" pipe than a 3/4" pipe.
The 3/4 pipe will give less frictional loss than the 1/2" pipe. The sizing of water through a house is of worked of


Main connection:  The total simultaneous demand in the house ( calculation given in a table for domestic houses which gives the nominal amount of flow to normal fixtures, or this can be worked out manually for non standard installation eg. a mansion)
The Main index run:The index length to the furthest (or most disadvantaged ( which in domestic is usually the furthest) fixture and the total loading units for all fixtures.
Branch Pipes: sized using the index length still and the loading units of fixtures on each branch
Branch from Branch: As above

Some things that affect the calculations are the available pressure at the main ( for main fed houses), the height of the house above or below main height (higher means less pressure, lower means more), the product used eg, materials have different frictional loss and i\d sizes. 


With the pressure increase it is good to keep in mind (which it seems you already understand), increasing the pipe size will not increase the pressure just decrease the frictional loss providing more available pressure and flow at the end destination.

If your interested in the calculations or regs have a look at this link for an example