I don't know whether it counts as "such a large part of the costs", but at least in the US it does appear that wages and fuel are about equal as the two major costs:
While fuel costs were historically the largest share of total cost, driver wages surpassed fuel as the largest share at 31 percent of total cost in 2015, and fuel now accounts for 25 percent – its lowest share since the inception of this study. Fuel was followed by equipment lease or purchase payments at 14 percent, with repair and maintenance, insurance premiums, permits and license, tires, toll costs, and driver benefits each representing 10 percent or less of average total marginal costs.
Tables 10, 11, and 12 show a more exact breakdown. If all else remained the same, removing the driver would appear to reduce total costs by 40% (30% wages plus 10% benefits). So unless the electricity is much cheaper than diesel it won't be "dirt cheap", but certainly would be a significant reduction.
While fuel costs were historically the largest share of total cost, driver wages surpassed fuel as the largest share at 31 percent of total cost in 2015, and fuel now accounts for 25 percent – its lowest share since the inception of this study. Fuel was followed by equipment lease or purchase payments at 14 percent, with repair and maintenance, insurance premiums, permits and license, tires, toll costs, and driver benefits each representing 10 percent or less of average total marginal costs.
http://atri-online.org/wp-content/uploads/2016/10/ATRI-Opera...
Tables 10, 11, and 12 show a more exact breakdown. If all else remained the same, removing the driver would appear to reduce total costs by 40% (30% wages plus 10% benefits). So unless the electricity is much cheaper than diesel it won't be "dirt cheap", but certainly would be a significant reduction.