Why not use TI’s BQ series chips, BQ series can use the BMS system to manage lithium batteries
This comment is meaningless: the bq series spans from simple chargers comparable to the MCP73831T, all the way to ultra-complex ones with full-fledged USB-C support and encrypted communication with in-pack BMS ICs. The bq line also encompasses the ancillary chips like fuel gauges, protection ICs (I dislike the term “PCM” because that abbreviation is already squarely spoken for by pulse-code modulation), and power switches.
And the OP’s battery pack doesn’t contain any kind of onboard chips with communication.
Why not use TI’s BQ series chips, BQ series can use the BMS system to manage lithium batteries
How will such a system be better than the proposed one?
Impossible to say, since they didn’t specify what they meant.
Anyhow, I believe your revised schematic should work.
Redundant protection works fine; in my current major project, we used protected cells during development just in case, but once the charging circuit (with its own protection) had proven itself, we used unprotected cells as envisioned.
P.S. The main purpose of the protection is against overvoltage (what if the charger malfunctions? Or if you accidentally miswire it? Or if a bit of wire shorts the DC in directly to it?), and overcurrent, especially short circuits. Undervoltage is a secondary function in a way.