As someone who has personally had to take those calls, they do matter. It just doesn’t matter what you say in the call: the only way your calls actually reach the politician is a tally sheet of each call received on different topics. End of the day/week, the politician gets told “you had X many calls about people wanting you to do this, Y many calls about people wanting you to do this, etc.”
Individual calls matter little, but if they get tons of calls on one topic then they take it seriously. The example above was probably during a time where the office was flooded with so many calls at once that they took the phones off the hook, which actually means that calls are working especially well. When the phones are blowing up, everyone in the office notices.
The best call to your representative does not involve you making an impassioned and well-argued case, because you’re probably talking to an intern. The most effective call you can make takes 15 seconds: “I am from [place in your district] and I am very pissed about [topic].”