solderdude
Grand Contributor
Basically, I am willing to spend extra $$$ is it is actually going to provide a reasonable improvement in sound,
The answer is no not very likely in your use case.
If you want to change/improve the sound you either use EQ or look for ear/headphones that you may like better. (the Shure is no slouch)
Personally I use FiiO DAP as my phone is a simple one (phone and SMS only) and like to have separate purpose made devices myself but can understand the desire to use an all-in-one daily usage device.