Why is the yield curve typically concave?

The normal yield curve is usually drawn concave. Why is this typically the case?

My current understanding is that long term bonds have higher interest rate risk because a higher percentage of its outflows come from coupon payments. For example, a 1 month bill price won’t change much for a change in interest rates since its price is dominated by the par value which will be paid back in a month.

Applying the logic to convexity vs. concavity: as time to maturity increases, the percentage of a bond’s price which comes from the final par value payout decreases slower and slower. Therefore, the risk premium should increase slower and slower creating a concave yield curve.

Is this logic correct or is there more to it?