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One interesting thing about home field is that baseball has historically had the SMALLEST home field edge.  (per Bill James circa 1987 -- so this might have changed).
As to reasons that were NOT mentioned above.  My take on home edge begins with the concept that only half of equation is home field advantage.  The other half is on-the-road DISadvantage.  Way back, I was doing a weekly NFL pick-em-all pool.  I knew of the +3 home default, but also knew some teams have larger PERSISTENT home edges.  So, I created a home/away grid, which split the edge +2 home and -2 road, (overstating the effect slightly).  I then adjusted the edge/penalty based on game results as the year progressed, (also adjusting raw power rankings, of course).  By season end, there were teams that were +5 at home and other -5 on the road.  IIRC, the biggest aggregate was 8 (+5/-3).  But, there were also a number of teams that moved the other direction, and ended the season at or near zero for one or both.
For pro sports, the #1 obvious factor regardless of the particular sport is TRAVEL.  Home teams get to sleep at home, dress as home, play with the kids ... there's a ton of non-sport comfort zone there.  Road teams have the actual travel, (jet lag is a real documented effect).  They also must live out of hotel rooms, deal with any number of travel inconveniences, and then go to their jobs.
But, I think the single largest factor is simply emotional.  Football and Basketball typically have much larger home edges.  But, they are both games that are fed by emotion.  Baseball is much, much more about control.  Much of baseball is about keeping your emotions in check.  So, the 50,000 screaming fans in Safeco don't necessarily help Ichiro at the plate.  They DO help the defensive end gasping for breath find the energy to blow past a lineman to sack the enemy QB in the 4th.
And a lot about emotion is simple belief.  When players BELIEVE they can perform miracles, then they can.  But, a lot of that belief is supported by familiar surroundings.  The player who has ALREADY come thru in the clutch before is more likely to do so again.  And playing 1/2 your games at home, MOST of those memories are going to be created at home.  But, there are occasional teams that become (usually briefly), dominant road teams.  This is likely pushed by belief.  You win a couple of come-from-behind road games EARLY in a season, and you have that belief system to draw on.  You don't have to hope you can win on the road, you KNOW you can win on the road.  But, different parks, different teams ... it's much harder to sustain road success over the long haul.