I understand your point and your right. It's just your numbers are off. At that point in the network your modem level is around 10 to 15 db of its original Tx power. ( Say a 40 Tx on a 20 tap, minus the 20 for the tap and another 5 to 10 for drop and splitter loss) So a - 3 db of noise and 15 db of modem signal would only give you and upstream SNR of roughly 18. Not good.
This is CABL.com posting #334968. Tiny Link: cabl.co/mbziS