The charger needs to use high enough frequency PWM and have enough smoothing to give reasonably "clean" DC out; you cannot just switch the power on and off. It needs very fine and very accurate control.
That should really be a fundamental part of the power unit, rather than an add-on, so a fault just stops the whole thing working, rather than a possibility of the add-on failing while the PSU is still giving full output.
I've been designing electronics as a profession for over 40 years and that add-on system is something I would not get involved with!
Lithium battery systems are inherently
extremely dangerous and need multiple levels of safety designed in to the charging and control systems.
Your bank of Lifepo4 cells has energy storage capacity equivalent to around 1/4 its weight of TNT.
It must be treated in all respects as if you were working with primed explosive, as it can do as much damage if something goes wrong, just not quite as fast...
Purpose made charger units designed for the job are not expensive, eg. first thing I found via google:
24S 25A 1500W LiPo/LiFe/LiTo Battery Charger
A bigger one:
To add to what Tony Stewart said - it's not the current in proportion to the battery capacity, it's the power in proportion to the BMS capacity!
The total input power with 22A @ 87.6V is near enough 2KW.
If eg. half the cells have reached full voltage and the rest are still in bulk charge, the BMS has to dissipate a significant part of the overall input, bypassing the cells that are at the correct voltage to allow the others to keep charging. The closer the cell capacity matching and the better the cell balance, the less wasted energy and the less work the BMS has to do.
For a serious large battery project I'd suggest adding the Daly active equaliser module to the BMS as well, to keep all cells in balance at all times.
And use high speed fuses rated at eg. double the maximum charge or discharge current, at the battery positive and at a couple of points in the cell series chain, to reduce the chance of a catastrophic failure if anything goes wrong in the battery bank.
Multiple levels of protection with redundancy are essential. You are risking your home and family otherwise.