If a potential client doesn't value your work, you can't convince them to value it. No matter how good your work is, the client values it based on what it is worth to them. A worse website might be good enough for their needs.

The only thing that you can convince a potential client of is that you won't work for less than your proposed fee. It's hard to walk away from potential work, but more volume of money losing projects doesn't make up for the fact that they are money losing. And a client promising lots of money losing work isn't worth keeping as an active client.

That's not to say never take a money losing project. Big established organizations with ample budgets often have orbital rings of larger and larger projects. The minimum overhead of working with them makes small projects in the outer orbit produce small losses. But small projects are the route to the orbits with bigger projects with obvious profits.