Sure, but I can replace "high COL" in your sentence with "like to drive Ferraris" and it is equally valid, and I don't think anyone will claim that the employer has to pay for my Ferrari affinity.
If you absolutely must get paid in Ferraris, you can go ahead and reject any job offers which don't offer them. However, the market of labor which must be compensated with Ferraris is non-existent, so employers don't have to offer this benefit to compete for talent. Everyone has a COL however, so employers do need to adjust for it to attract employees in a given location.