Why are modern commercial airplanes still so noisy?
Like everything in aviation its a trade off of a few factors. 

Efficiency: A non-running engine is pretty quiet but that's of little use to a pilot who needs thrust to actually go anywhere. Now you can have lots of sound suppression in an engine and alter the airflow and what not but in the end of the day jets work on Newton's third law so you still need to throw a hot mass out the back. Any attempt to baffle this will take a toll on efficiency. (Side note, car exhausts have a similar effect on car engines these days). 

Weight: The generally accepted way to reduce noise is to insulate against it. What you are really doing is adding material to absorb the mechanical energy that is the sound wave and dissipate it. Generally this is done with insulation of some kind (there is a variety of styles). But like anything this takes a toll on weight and will reduce what you can carry. 

Cost: Insulation does wear out and break down over time (its usually some kind of foam), so the more you have the more you need to replace. Also of importance is the fact that most of it gets removed during check to inspect the airframe so having a lot of insulation will add to your down time during checks (this costs the airline money in terms of hours).

If you take a look at some custom-built private planes you will see some of the things they can do in terms of added noise reduction and what those implementations look like. On the other hand active noise control is becoming a cheaper and more efficient technology in headphones which makes a case for not needing to improve insulation (it will eventually be cheaper to have a pair of ANR headphones for everyone than maintain a lot of insulation). A lot of the GA community has moved to ANR headsets which are much nicer than their traditional counterparts.