That is not true at all. There is an extremely well established principle in English common law jurisdictions, including Australia that “the successful party is generally entitled to his or her costs by way of indemnity against the expense of litigation that should not, in justice, have been visited upon that party.”[1]

[1] Northern Territory v Sangare [2019] HCA 25; 265 CLR 164 at [25]

What!? Costs awards are the usual practice in Australian civil litigation.

and worse, even when they are "covered", the cost assessing process does not remotely cover most of your legal costs.