Why does flying IFR require a rating?
The short and sweet answer to this question:  That kind of thinking is what kills a lot of pilots.

A non-instrument rated pilot may know how to fly and navigate but does not yet have the skill to do so in total reliance upon instruments.  A PPL does require you to have at least 3 hours of simulated instrument flying with an instructor.  That may keep you alive in straight and level flight if you enter instrument conditions inadvertently, but it's not going to be adequate for conducting an entire flight in IMC.

This quickly becomes clear to new students pursuing an instrument rating who go for their first filed IFR flight in hard IMC with an instructor.  Once you enter a cloud, you go into a world of brilliant white (day) or inky black (night) and there is absolutely no visual references to follow.  You must be able to stay on top of that airplane, manage all of its systems, communicate with ATC, fly departure and approach procedures correctly, and handle emergencies, all without the benefit of visual reference.  In addition instrument flight has a nasty habit of inducing sensory illusions and spatial disorientation due to vestibular sensations causing the pilot to incorrectly judge the aircraft's attitude, etc.  You will be surprised the first time that you fly in real IMC just how STRONG the urge is to trust your vestibular senses over cockpit instruments and you can start doing this unconsciously when you start getting saturated and overloaded with cockpit tasks like terminal environment workload, emergencies, and delays and holding.

A number of pilots - good ones too - are now dead because they did not take this seriously.  One notable high profile case was John F Kennedy Jr., who inadvertently entered instrument conditions during a flight from Essex County Airport in NJ to Vineyard Haven, MA.  Even though the entire flight was in VMC, dark night over water provides no visual references for the pilot.  Kennedy became spatially disoriented; his PA-32 Saratoga entered a tight spiral and crashed into the ocean.

When I was prepping for a solo CC with an instructor for my PPL (the flight was scrubbed due to weather that day) I watched a guy take off in a PA-32 Saratoga and kill himself by flying into inclement weather.  The weather for that day had 600 ft ceilings and poor visibility.  He attempted to scud run under the deck, became spatially disoriented and flew into an antenna park near the Arkansas river.  The plane was sliced in half by a guy wire and crashed.  The pilot was not instrument rated but filed an instrument flight plan, departed KRVS with a clearance, then deviated from the flight plan and attempted a scud run.  His desire to fly his family down to Dallas to see a college football game in bad weather without proper training for it killed himself, his wife, his two teenage daughters and a family friend.

It takes a lot of practice to successfully fly in IMC.  The FAA required instrument ratings for pilots to conduct instrument flight due to the high number of accidents associated with inadvertently entering IMC or worsening weather conditions without competence in instrument flight.  Over 80% of these kinds of accidents result in fatalities.

In addition to requirements to becoming rated for instrument flight, per 14 CFR §61.57, the FAA also has currency requirements to maintain instrument proficiency.  You are required to have executed at least 6 instrument approaches, holds and navigation by electronic nav systems within the preceding 6 calendar months.  This currency work must have been done in either real or simulated instrument conditions.  Once that expires, you do have an additional six calendar months to complete this currency work with safety pilot.  If after 12 calendar months you have not maintained this instrument proficiency, you must undergo an instrument proficiency check with a CFII.

UPDATE - in regards to advanced, modern avionics in the cockpit, back 18 years or so ago when I was a young engineering student and the industry was beginning a transition from traditional structural analysis calculations done by hand to using computer aided finite element analysis programs, a college professor of mine once made a comment that always struck me as very applicable to advanced integrated flight decks.  He said that these new FEA programs had the capability to make a good engineer better and a poor engineer dangerous.  I’ve always viewed modern glass cockpits in the same fashion and accident statistics on this seem to bear it out as well.  Glass cockpits and modern avionics can improve your ability to fly an aircraft, reduce pilot workload and fatigue during critical times but they can get you into a lot of trouble as well.  There have been many cases where pilots have run out of fuel and crashed or had a fatal CFIT simply because they did whatever the screen told them without being able to critically think about what information they were receiving and cross checking it to see if it made sense for a given situation.  Autopilots and autothrottles, too, are useful for relieving the routine grunt work of flying, but can result in emaciated stick and rudder skills, which will be needed in critical moments should an AFCS fail.

An instrument rating is nothing more than a journeyman's license to practice instrument flight.  One should always be aware of this and approach the process of planning an instrument flight accordingly.  All it takes is one harrowing incident to really scare you up and make you aware of you own human limits and mortality.  Set personal minimums for flight conditions and approaches well above published minimums and periodically evaluate these as you continue to build experience.  Never fly an approach into an unfamiliar airport or one surrounded by mountains or other hazardous terrain until you have done so in visual conditions and practiced the approach on a day VFR flight.  Be wary of the differences between flying IMC in day or in nighttime.  Be cautious of instrument flight in busy airspace eg the SoCal Class B areas, etc.  These are just a few of the additional challenges and hazards you need to consider before you venture into darkened skies...