The ontimeflights site creates a strawman argument by purposefully portraying ATC technology as being decades out of date. As of 2015 all 20 Air Route Traffic Control Centers in the continental US upgraded to
ERAM - The Nextgen ADS-B compatible replacement of the old HOST computer system. Most also no longer use "paper slips" (flight strips). They're also obfuscating the overall point in stupid analogies. "Can you believe ATC doesn't use basic GPS technology like what's in your smartphone today?" (Actually I can you morons, I'm all for ADS-B supplementing the ground based radar system, but getting rid of it entirely will be really bad news when other traffic forgets to switch on their transponder, or hijackers intentionally switch it off, etc. Plus the deadline for implementation is 2020 and hasn't even happened yet.)
I took a tour of Los Angeles ARTCC last month and was blown away. It was my first tour of an enroute facility, and other than being generally impressed walking into a room of more than 100 people on the midnight shift, I was really surprised by all the ERAM upgrades. The Traffic Management Unit (TMU) is like floor to ceiling LCDs showing the status of the NAS, and other than oceanic (which shouldn't count

) paper flight strips are totally gone.
This is the overall setup post ERAM, D-side on the left and R-side on the right (this photo was taken in an ATC lab but contains the same equipment):
The R-side is the radar controller that talks to aircraft and separates them by radar. The D-side is the assistant controller for that sector. My original understanding of a D-side was someone who squinted at and shuffled flight progress strips around, and answered interphone calls. These days the flight strips have been replaced with an LCD screen called URET, and the D-side uses URET as a tool to try and predict downstream traffic conflicts based on routes and time (ETAs over fixes, etc) and resolve them before the R-side ever sees them.
More on URET:
http://automation.forthillgroup.com/story/URET
The thing that kept surprising me about the enroute environment was how much emphasis is put on solving problems before they happen, and how the TMUs work to reduce congestion at a certain airport by working upstream to institute gate holds at the departure airports (the alternative of sitting in holding patterns on STARs until minimum fuel is worse).
So for you guys griping about NextGen and privatization of ATC being the silver bullet that will get rid of gate holds - your argument has no basis in reality. The traffic capacity of the national ATC system is a known thing, and as soon as it reaches capacity the cogs in the machine spring into motion and start working backwards up the chain to kill the problem at its source (gate holds).
While controller staffing and training plays a role, the overall problem is every airline scheduling the same departure and arrival pushes at the same times - there's only so much pavement you can use for takeoff and landing, and so little lateral and vertical separation you can put between airplanes.
This is the disfunctional price you pay for a "free-market", de-regulated airline industry.