Manufacturers really don't care too much about shipping costs (and the secondary CO2 burden) once the machine leaves their loading dock. Their concern is to make the machine as cheaply as possible for the features involved and maximize the margin.

Costs are probably not that high anyway. For most logistic companies, volume determines capacity for trucks, not weight. Transporting a washing machine amongst other deliveries will not cost much more than other deliveries of that size (except for the additional fuel which is probably low). Carrying it in place can be done within minutes, not much longer than other deliveries.

That's probably also the reason why machines are cheap to buy online. If shipping was a constraint, buying at big stores would be cheaper.

Therefore, concrete can save some CO2 but probably not much cost. The cost of replacing faulty water tanks could be higher than the saved cost.

This. The problem is that the costs of transportation are externalized to a shipper, and the environmental costs the shipper incurs are externalized to ... future generations? And the cost of the eventual replacement is externalized to the consumer ten years from now. It may be wise for us as a society to find ways to fully account for all costs of products to use market forces to make better decisions for society as a whole, rather than enriching a segment at the expense of another.

then fill it with concrete..

Better question - why can't we reuse the concrete blocks.