He says it's ok NOT to terminate charging, that it won't hurt the battery if the charger continues to apply 4.2V to a fully-charged battery. That goes against everything I've learned about lithium batteries. Also, if he's right, why do all lithium chargers I've ever seen include a termination feature? If continuing to trickle charge is ok, why bother to terminate?
Lithium batteries, definitely no - they can't be charged.
But let's talk about lithium ion batteries. He is kinda-sorta right. Li-ion battery is close to an ideal battery, which is a voltage source with some very small series resistance, and very large parallel resistance (self-discharge). The voltage of said "voltage source", also called open-circuit voltage (OCV), is a function of the State-of-Charge (SoC); for example, 100% is 4.20V and 0% is 3.40V and 50% is 3.65V. Not a straight line, but kinda close.
Now if you apply 4.20V to a cell which has open-circuit voltage of 4.20V, by simple Kirchoff laws, no current flows, except the tiny current equaling the self-discharge current.
There is tiny nitpick - manufacturers do not define 100% SoC as 4.20V OCV, but instead like "100% is when C/20 flows at 4.20V terminal voltage". Equivalent OCV is a bit smaller, like 4.17V. By floating indefinitely at 4.20V, you are thus keeping the cell at something like 101% or 102%. Hardly a problem, but do the tolerence analysis. If your voltage supply is inaccurate, better derate the voltage more.
Now why is it shunned? #1 reason, by far, is the shitload of pseudo-"information" by people who have absolutely no clue what they are talking about, and fake information sites like Battery University. But to be fair, they have a point. Cell manufacturers also instruct to terminate charging, not only with a stopping current like C/20, but also a timeout.
This is because manufacturers have thoroughly tested their products in "typical" use case, and that typical use case is charging a cell, then disconnecting the charger anyway, and starting to use the thing, until it needs to be recharged. In such use case, it makes no sense to float the cell indefinitely. Li-ion cells do not self-discharge much anyway, so no need to "keep it topped". It keeps topped on its own.
Terminating the charge with a combination of C/20-like stopping condition plus CV phase timeout, offers one simple check against a specific cell failure mode: namely skyrocketed leakage current due to internal failure in cell. If the cell consumes more than C/20 on it's own, by just being, CV phase never finishes, timeout triggers, and amount of charge put into the cell is limited. I'm very skeptical of this being of much use, but it's
something. By floating the cell indefinitely, you bypass this.
But an internal short inside the cell finally causes a
thermal problem, and some 2-hour timeout can't help with that. Temperature sensor is much better at that. And if the internal short is not enough to cause significant heating but trigger timeout, then the user sees some blinking red light, continues to use the cell anyway, and recharges it again, bypassing the result of this safety check. Unless you store "this cell is faulty" information in non-volatile memory, but neither the manufacturers nor the Battery University scientists require you to do that!
In real world, li-ion cells
are used in float charge configuration (always connected to a CC-CV supply), despite all the Battery University Internet Scientists saying otherwise. It's just this use case is not widely documented and not supported by the cell datasheets. You need to discuss this with the cell manufacturers to be sure. And the voltage won't be 4.20V, more like 4.10V.