No it shouldn’t. The pressure in your home depends on many variables. Much of it depends on how much pressure is coming to your home from your city system, usually between 40-85 PSI. You may have a restrictor at the main valve of your home if the city pressure is above 80 PSI. Upon coming into your home, pipe size reductions and build up in galvanized water pipes can affect pressure as the piping is distributed in your home.
Most new shower heads do have flow restrictors built in them to reduce water consumption down to 2.5-1.8 GPM (gallons per minute). These restrictors can be removed in most shower heads but many states have regulations that require low flow fixtures to be installed when remodel work is done under permit in older homes, as is the case in my home state of California.