The cost should not be that much different. In fact, you might find that it is cheaper to do it after everything else is done. First, your builder will likely subcontract the work and add a percentage to the project. Second, and I see this all the time, if irrigation goes in too soon, it often gets broken during construction or needs to be revised due to changes in the landscape that occur as the project progresses.
This point is pretty much moot, however, if you've got new trees, shrubs, or turf in the ground that need water before the end of the project - as is often the case.
It also isn't too disruptive to install after the fact. Contractors make a slit in the ground to place the lines. These typically heal to "invisible" within a few days to a week as long as the job was done by someone experienced and with the right equipment.
On the question of whether it is needed, there are a range of answers. We are fortunate to receive a fair amount of rain where we are in NY, so we typically only install temporary irrigation on trees and shrubs to ensure they get started well (most of our clients don't want to hand water until then). The drip lines are then removed after the first or second year. Some water demanding shrubs, hydrangeas for example, need it perpetually. But we try to steer clients away from plants that won't do well on their own in the local environment, preferring native and hardy species. Plant selection can therefore reduce the size and cost of your system.
Turf is another matter. Until late in the 1900's, even estate cool-season (bluegrass, fescue, etc.) lawns were left to go dormant in the high heat of August, and irrigation wasn't required. The lawn would green up in the spring, go dormant for a month or so in the summer, then green up again in the fall - it's the natural cycle of cool-season grass species. However tastes have changed and people want actively growing, green grass throughout the season now.
Turf choices and management practices can also have dramatic effects on the amount of water a lawn requires. A fescue lawn left long (3" - 3.5") might not need irrigation at all around here. Your extension office will likely know what grass varieties do best in your climate, and your tolerance for natural variation may dictate the need for irrigation at all.