Power supplies are one of the most expensive component in an audio product. Upgrading an inexpensive power supply often results in improved performance.
^^^^ this.
Upgrading from a cheap wall wart is a no brainer on an evolved system. How much of a difference you'll notice is a variable, but it should be a step in the right direction.
I don't have a specific recommendation on a brand, but have replaced the wall warts on my phono stage and DAC with DIY regulated linear power supplies, and offered lower noise floor and more refined overall performance in both cases.