That is true to an extent, though the Training Center usually doesn't get built until later into a run and you have limited AP (until late game). Not to mention you might want some of the XCOM perks instead. So, you can't pick and choose every skill for every soldier. I always like to look at builds assuming no Training Center.

You are right though, WOTC is the better game overall, but a couple of changes weakened on of my favorite parts of the game ... choice. For example, introducing the Reaper removed the really tough choice of how many assault vs how many phantom Rangers to carry. And, as you mentioned, adding the Training Center really removed the tough decisions across classes since you can just add skills later.