Why are multiple infusions of tea better than one large one
the combination of two infusions would be the same as doing one infusion for longer 


That's not how it works. The leaves are full of different chemicals that are locked away in cells and their organelles, behind several membranes, and they have different solubility. So there are multiple effects which make many infusions different than one big infusion. 


Nernst's law. When you extract something, the concentration gradient plays a role. When the tea outside the leaf saturates, chemicals stop exiting the leaf. 
The one that you mentioned, about tanins. They don't "pick up where they left". To use an analogy, imagine having a piece of ice. It is big enough that you have to keep it 10 minutes at room temperature before it starts melting. Now, if you keep it out for 3 minutes, then put it for some time back in the freezer, then take it out again, it will again need 10 minutes to melt. (This is not to say tanins melt the way ice does, just to remind you that there are plenty of processes which don't somehow continue after being interrupted). 
You actually do have other flavors coming out which you wouldn't get with the new infusion. Opposite to tanins, there are some chemicals which start being amenable to extraction the first time they come in contact with the hot water, but won't extract much at the beginning. Staying wet while waiting for the next extraction prepares them to get out in larger amounts. 
An effect similar to the last one happens to the cell walls that prevent chemicals from getting extracted. They soften with the time they spend warm and wet - which, in the sum with multiple infusions, is larger than the length a single "large" infusion would take. 
Different taste in the different infusions. Since a different proportion of each type of chemical comes out in each successive infusion, people get to enjoy different flavor profiles. A single long infusion would have the same taste throughout.