I see that I can set the banding limits for a Tariff Line Item to be specified on the Meter Account Edit page instead on in the Tariff page.
But why are there still banding limits on the tariff line item when I choose for the limits to be specified on the Meter Account Edit page instead? What must I set these values? Must I set them to 0?

No, set the limits to the 'default' values. The defaults will be used if the Meter Account has not been set up with limits.
Please make the defaults realistic values, so that the billing engine will not throw out the line item. Do not specify all zeroes please.
If you enable lets say 2 consumption tariff line items for 2 different bands, and set both to get their upper and lower limits from the Meter Account specific Edit screen, there will be 4 limits to be set up on the Meter->Edit screen:
Each line item will have an upper and a lower limit to set.
For the lower band, the lower limit should be 0 (zero); and the upper limit the banding value (e.g. 40).
For the upper band, the lower limit should be exactly the same as the upper limit for the lower band (e.g. 40); and the upper limit should be something very high, that will never be reached, e.g. 9999999999