To start: I understand what this error means - I'm not attempting to resolve an instance of it.

This error is notoriously difficult to troubleshoot, because if you get it inserting a million rows into a table 100 columns wide, there's virtually no way to determine what column of what row is causing the error - you have to modify your process to insert one row at a time, and then see which one fails. That's a pain, to put it mildly.

Is there any reason that the error doesn't look more like this?

String or Binary data would be truncated
Error inserting value "Some 18 char value" into SomeTable.SomeColumn VARCHAR(10)

That would make it a lot easier to find and correct the value, if not the table structure itself. If seeing the table data is a security concern, then maybe something generic, like giving the length of the attempted value and the name of the failing column?