https://www.investopedia.com/ask/answers/accrued-interest-why-do-i-pay-when-i-buy-bond/ This seems like a bad custom because it creates a lot of unnecessary counterparty risk that persists for up to a year after the trade. Anybody who owns the bond after you might default when it's time to pass on your share of the interest. On the other hand if the owner were entitled to the entire coupon, the previous owners would implicitly get paid up front in the form of rising prices between coupon dates. There would be less counterparty risk and a more favorable tax treatment (replacing interest with long term capital gains if you hold a bond for a year and then sell it shortly before the coupon date). Administrative costs would also be lower.
Or maybe the DTCC handles splitting up coupons so there's no additional counterparty risk arising from the chain of custody. Does anybody know?