Morally you might be right, but that’s not the legal definition.
Your tips are counted as part of your wages. In some cases companies can pay wages below minimum wage as long as the sum of wages and tips adds up to minimum wage.
> In some cases companies can pay wages below minimum wage as long as the sum of wages and tips adds up to minimum wage
Both federally and in many states wage and hour laws, there is a lower tipped minimum wage that can be paid so long as the sum of tips and actual wages is at least the the level that would be the minimum wage for a nontipped position, but the fact that there is still a minimum for the actual wage and that the wage is summed with tips to compare against a separate target makes very clear that “wages” and “tips” are separate buckets, the former does not include the latter.
Now, there are other things (like income taxes) that operate on the sum not one of the individual buckets, but that's a different issue.
> but arbitrarily excluding wages from someone’s earnings
No one's excluding wages from earnings, or tips from earnings; what is excluded is tips from wages, just as is done when setting a separate tipped minimum wage (that only is a minimum for wages, not wages plus tips), like the federal $2.13 and many state wage and hour laws for tipped employees, or when setting a minimum wage and not counting tips against it (as is the case in a number of US states and territories, including Washington, California, and others.)
Your tips are counted as part of your wages. In some cases companies can pay wages below minimum wage as long as the sum of wages and tips adds up to minimum wage.