I use separate components: Batteries, charger, inverter. With separate components, you can choose exactly what you want for each task specifically for your use case. If any part of the system fails, you can address that component individually. Further, you have much less software/apps/BS to confuse the operation, and it turns out to be about half the price of a Delta or similar. Plus you can simply expand your battery bank however you like so long as you can make cables and fuse everything properly, which is not difficult. Overall just more flexibility.
I keep it fully charged on standby for grid-power outages, then use a 2kw Honda for charging if the grid is down for more than a few days. I run the generator at about mid-load as steadily as possible, on a 12 gauge 100ft extension cord so I don't have to hear it. If the generator surged from an erratic charge load as you describe, I would go completely nuts.