On-the-run Securities and Liquidity

I have seen words like “On-the-run securities are always considered the most liquid” from several places, and am just wondering, is this always true? And why would this be true? Why do people prefer the on-the-run to the off-the-run? Could there be a situation where off-the-run securities are more liquid than the on-the-run ones? Thank you!

On-the-run bonds tends to have coupons that are close to current market rates, while off-the-run bonds may have coupons that are quite different from current market rates.

Having cash flows that closely approximate market rates is arguably a desirable feature.

Would you mind explaining why having cash flows that closely approximate market rates is desirable feature a little bit? I did not get it. Thanks!