Interesting article. Regarding the paradox of semicolons on CTEs - the rule is "the statement before the CTE has to end with a semicolon". The reason is that the WITH keyword is overloaded in T-SQL. Without the semicolon, SQL can't tell if you're saying with as a statement start or qualifying something about the previous statement.

People have gotten used to putting a semicolon in front of the WITH, but this is not required - you can just as easily put it at the end of your last statement.

This also explains why this causes an error in an inline Table-value function. Inline table-value functions must be only a single statement. Therefore if you use a semi-colon in it (which is the statement terminator symbol), then you are causing the TVF to have two statements and it breaks.