The logic of if you have to ask...you don't need it...is flawed. There are plenty of questions and answers that may need to be understood for decision points or to weigh how the scenario may apply to oneself.
4*4 is nice to have, do you need it..probably depends on the area you live in and where you plan to travel. Yes you can get stuck on wet grass with some trucks...as dumb as that sounds. (2wd). All situations can't be dealt with the old-school idea that I was driving before 4wd was created. You can get stuck with 4wd too...
There are way too many variables to give a solid answer....most likely if you stick to the pavement and lower elevations and avoid extreme weather then 2wd will serve you well.
At some point the weight and conditions will get the "old-timers" too. Its hard for me to believe that unless you camp in the wal-mart parking lot...that you have not gotten stuck... that is unless you only travel in the summer and you stay below the snow line and are on hard surfaces 100%. Will 4wd solve all your issues about getting stuck..no! A trailer generally magnifies your problems...especially traction (snow/mud/ice)although weight is an asset at times....all depends on the situation. Of course if the trailer swings around and tries to jack-knife....its time to really question if you should not be stopped somewhere.
I have a 3/4 ton truck 2wd 2500 HD and I tow about 10K... I watch where I go and where I can back up etc... A 2wd will probably be a 99% solution....for most of the time. I stick to the hard ground when on grass (off the pavement or gravel). The tow rating for 4wd is reduced by a few hundred pounds due to the weight of the transfer-case...and front end components.
4wd will be on the next truck I get...it can make the difference in moving at times.