I would argue those prices a bit. A pair of 5kWh rackmount LFP batteries is only about $3,000. Assuming you're charging overnight, you can definitely get by with a 120V inverter like OP. Get a charger that does NEMA 5-20 for 16A and it'll transfer 10 kWh in 5 hours overnight fine.

I agree with your conclusion that wall is better though.