I think the big problem with a charge pump will be, the voltage difference is very small (10s mV at end of charge/balance) and gain is only ever exactly 1 (minus loss); you don't have any way to overcome losses and deliver a controlled current between respective cells. And cells are effectively such massive capacitors compared to anything you'd put in circuit, not that balancing requires much work on average, but it may still require enough (and MOSFETs too) that it's not practical versus other methods. It also diffuses the charge imbalance into neighbors, rather than either dissipating excess directly (practical as we're only talking a few percentage points of lost efficiency even in a rather unhealthy pack, and an even more unhealthy one just shouldn't be used anymore), or redistributing it evenly to the remainder.
At least ESR isn't hard to come by; a 10uF X7R will still have plenty of value even in 0805 size, at 4.2V. 10uF might have to run pretty fast still (say, a MHz for <20mOhm), so probably a somewhat larger size would be chosen (100uF?) or enough used in parallel, or electrolytic (even bigger to keep ESR down), or maybe polymer (if economical). MOSFETs aren't a problem, indeed it's almost a problem if anything that they're hardly available at low enough voltages to keep Qg nice and low. (IIRC, selection is narrow -- but indeed available.)
Gate drive -- would you use a DC restore network and just drive them all ganged together? Hmm, has some possibility. Hot-plugging, or first time wiring the balancer to the pack, might be an interesting experience. Maybe that's fine with some clamp diodes. Maybe a precharge circuit (all taps are wired up through modest value resistors first, then shorted out).
Reliability -- would probably want to use fancier ceramics (flexterm, short resistant) if they are to be wired across the battery at all times, if this is internal to the pack that is. Taps can be fused, and, any tap blowing needs to be sensed by the controller as a failure. (So, don't just keep the charge pump running mindlessly such that the controller reads perfect balance across a missing tap!)
How much is actually needed -- not sure, depends on the relative impedance of the cells during charge. I've not designed a balancer before so that's something I'd need to look into. Maybe it doesn't need to be the mOhms I imagine it does (say for a small pack using 18650s, or the next one up). Then again, there will always be some scale of battery pack where even mOhms is too high, and perhaps an inductive buck-boost topology would be warranted above some point (in which case, where is that point?). Or alternative strategies applied, like disconnecting entire affected cells (total battery voltage fluctuates over time), whether for purpose of individual attention (charge/balance), or self healing (out of spec, removed permanently from battery), in which case multiple such batteries could be wired in parallel to achieve arbitrarily high total Ah or Wh, using a converter to address the variable output voltage and deliver a fixed common bus (or perhaps widely variable as the case may be, e.g. for a VFD).
Perhaps the video goes over these finer points, I don't know.
Tim