What an odd time to do it, unless for some crazy reason the lat/lon location mattered.
I'm just saying it takes less than a second to hit a ditch or another plane or commo tower while taxi-ing on the ground. Or suddenly do almost anything when you're 50 feet off the ground at takeoff surrounded by all sorts of interesting ground targets to hit. Drop the landing gear or flaps at the wrong speed at a low altitude. I suppose someone indecisive or having medical / drug issues could take a long time to talk themselves up to it hours into the flight.
There is one situation I'd expect a crash halfway thru climbout right after takeoff and from military experience if a load is incorrectly lashed down in the cargo hold and lets say the strapdowns in the front of a tank or howitzer are installed correctly but the ones in the back snap or were incorrectly attached or the tiedowns rusted off LOL (I suppose it happens) then sliding a tank or an artillery piece thru the nose of the plane while in flight will make quite a mess. Yes I'm well aware a civie 737 is not a military C130 but the general case holds that's just about the right time in a flight profile for something in the cargo hold to start sloshing around if not strapped down correctly.
Plenty of opportunity for cascading failure. Trivial to engineer a cargo system where one thing breaking loose cannot screw up weight/balance enough to crash the plane. But one thing breaks loose, slides at high speed into another thing breaking it loose, now you got two uncontrolled loads sloshing around in turbulence, repeat, repeat...
I'm also well aware that a 737 is not a military transport in WWII but there was a documented problem with sabotage in WWII where enemy agents dumped water into the rotary engine oil system and the water eventually boiled about ten minutes into flight, steam popped open the oil system, the engines seized without oil, the mechanics got blamed and the agents continued their work because no evidence just water... Obviously almost certainly not the situation now, but the general idea of "it gets up to full temp a couple minutes into flight" remains valid. I wonder what happens to the airframe if an engine bearing catastrophically seizes and cold welds itself in flight. At minimum I bet the entire engine tears itself off the pylon. Worst case maybe the engine takes the wing with it even if its not supposed to. AFAIK the shroud around engines is supposed to be able to eat a turbine blade that snaps off to prevent damage to the wing, but maybe there's a freak situation of the engine disassembling itself in flight such that the shield shroud thing is blown off milliseconds before the turbine blades are shed into the wing...
I'd extend my remarks based on radar data from
http://www.b737.org.uk/incident_pk-clc.htm
This is a very low performance aircraft (In the sense of not like a F-16) and 11 seconds isn't long enough to intentionally maneuver from a normal climbout based on radar transponder data into falling out of the sky. A F-16 could turn 40 degrees and point straight down in 11 seconds but a 737 literally can't, so essentially it went from a normal climbout to cloud of parts falling from the sky slower than the plane at cruise. The radar transponder profile looks a lot different for a plane in one piece under control pointed at the ground. Pieces of aircraft are not aerodynamic at all, which is why parts fell at 10K to 20K feet/min but the groundspeed collapsed from 300 kts to 100 kts in eleven seconds. I'm honestly not sure even a F-16 can drop from 300 kts to 100 kts in eleven seconds in a steep dive, although a random collection of torn metal falling from the sky can do that.
Its interesting that if you google for the flight manual data for a 737, best maneuvering speed to handle maximal turbulence loads is just a couple knots below best climb speed, which the plane was at. So if a pilot was suicidal, he tried to pull the wings off at exactly the flight condition where the plane was strongest; no pilot is uneducated enough to make a noob error that huge. Pull up as hard as you can at cruise, sure. Wiggle the rudder as hard as humanly possible (usually due to crosswind) while landing has torn tails off planes. But try to pull the wings off when flying at manuevering speed? That's just dumb. So no the pilot almost certainly was not suicidal.