You misunderstand, hun. Trixie's profession is to impress with powerful magic capabilities she does NOT have. Her magic is what many would consider weak. She didn't "decide" to be arrogant and fake. She's like that for reasons that aren't known to us but it doesn't hurt to take certain guesses. Some believe she is the way she is because she insecure that she's a unicorn with weak powers.....and tries to hide it behind a mask of pride which comes out as arrogance to others. It's called impressing the people with illusions and lies. The illusion is making it seem as though she is far more powerful than she actually is. And the lies are, of course, stories to make a reputation for herself and back up her illusions. Even in a world of magic being common, ponies seemingly are still impressed by magic itself. In fact, "power" seems to be a big deal within the FiM series anyway. The powerful you are, the better your reputation. And quite frankly, reputation, whether it's in this world or theirs, is EVERYTHING.
There's nothing wrong with considering her profession as a joke. Regardless, it is her profession. Many say Rarity's profession is a joke because she dedicate herself to clothes which isn't a big deal to wear in the pony world. Same for the Pegasi....where their profession is to control weather, but it's been implied many times how unicorns are able to control the weather as well. In fact, many daily tasks can easily be done by "magic" from unicorns: baking, clothing, weather, building, even the rise of the sun and moon. Granted, it'll be difficult, but NOT impossible for any of these. One could then say that any other pony who performs these tasks as their profession are "jokes".
Her goal isn't to prove that magic is real "yo give me money because I am a real unicorn performing real magic". Her goal is to prove she's more powerful than the average unicorn "yo give me money because I'm the most powerful unicorn in equestria".