I understand that the break angle is different. I have had problems with a steep break angle going through the body on a B string. By itself, I don't see what the break angle would have to do with stiffness or tightness. If the second part of you supposition, that a lot of string length allows more "stretch" when you bend, wouldn't that imply that top loading or tailpiece loading would make it easier to play out of tune than with string through?
Break angle has nothing to do with tightness. It only affects perceived stiffness.
Extra behind-the-bridge string length makes it (in theory) easier to bend strings when you want to bend them. Playing out of tune is a matter of bad technique, regardless of how bendy your strings are.
Think of it this way, and I'm not the first one to frame it in these terms: If you had 3 feet of string length between the nut and the tuner, a standard scale length, and then another 3 feet between the bridge and tailpiece you'd have 106 inches of total string to stretch when you bend a note. If you then clamped the string at the nut and bridge and cut off all the extra it would be at the same tension and pitch but it would be more difficult to bend because you'd only have 34 inches of string to stretch.
Similarly, if you think of a string going over a bridge saddle with almost no break angle there's less force pushing the saddle down towards the body than if there's a 90 degree bend immediately behind that saddle. Its the same reason there are string trees on Fender headstocks. Break angle and downforce makes strings work and feel different.
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