Having the precast stair installed as early as possible in the process makes a lot of sense to me, especially given the alternative is to use some kind of ramp.  Safe entry to a job site becomes more important as the number of risers increases, but even this job, with just an easy two rise, benefits greatly from early install.

Here is a lengthy but likely not comprehensive list of the benefits of early install of a precast stair at the job site

1. Safer access - in any season, but especially winter, a ramp can get very slippery.  there are many hazards already on a job site so this eliminates a big one
2. Inspector friendly - city inspectors may not enter the project to inspect it without a safe entry in place.  Why bother building a ramp and putting handrails on it when you can just have the precast installed weeks earlier?
3. Deliveries - it is much easier to delivery everything from lumber to pipe if the stairs and landing are in place.  the precast will assist every trade from start to finish with getting tools and material in and out
4. Exterior finishing - the stairs need to be in before exterior work such as stucco or siding goes on.  This way the flashing can be done more accurately around the precast.  
5. Cleaner project - less mud will get tracked into the house
6. Sidewalk planning - once installed the front grades and requirement for the sidewalk is easier to visualize and the precast also needs to be in place before formwork on the stairs can begin