...some were saying that it's possible for the phases to get unbalanced, and the unit shuts down in protection mode.
There's a
video about it that might help.
The issue is a split-phase power issue. In North America and a few other places the power is what's known as "split-phase".
Off the power pole coming into the house, most people have 3 wires commonly called L1 (aka leg 1), L2, and neutral. Voltages from L1 or L2 to neutral is 120V, and voltage from L1 to L2 is 240V. In your fusebox, the breakers that are two breakers thick are 240V, the skinny ones are all 120V. This allows most of the house to have lower voltage and be "safer". EU, Austrailia, and most other places are single phase 220V.
Ideally, if a house is usually pulling 10 amps, the electrician wires it targeting to have 5 amps on L1 and 5 amps on L2. Or they should, but it's not that big of a deal while on grid. But, if a 12 kW inverter can only put 6 kW on L1 and 6 kW on L2, an owner is sometimes surprised they can't get 12 kW on a single leg.
In the Sol-Ark 12K case, it's rated for a maximum 240V current of 33 Amps (9 kW) and a maximum 120V current of 40 amps (4.8 kW). So, if a 120V pump has an inrush of 60 amps (7.2 kW), it's likely the inverter will reset rather than supply the power. A neutral forming transformed can be used to help shift some power between legs, but you take an inefficiency penalty.
...Apparently the Sol-Ark is beefy enough to be installed in front of the main...
Be careful about that. You might only be pulling a few kW in "survival" mode, but in normal use, with a dishwasher, washing machine, air conditioner, TV, computers, etc. the loads can be quite high for brief periods. Most homes have 200 amp meters and a 150 to 200 amp rated fuse box.
In the Sol-Ark 12K case, it's rated for a 50 amp passthrough, which is a far cry from the normal 200 amps.