Dedicated current sense amplifier vs simp,e difference amplifier
What are the specific advantages of dedicated CS amplifiers?

Current sense amplifiers are designed to operate from a low source impedance, so they can have lower input impedance than opamps, which allows topologies that offer features not available to opamps.
Among these the most interesting is the ability to operate with input voltages way beyond the power rails of the amplifier. This is extremely useful for high-side current sense.
You also get convenience and cost features, like having good offset and CMRR without having to buy expensive matched precision resistors.
These features are very useful for a high-side current sense, but not for a low-side current sense. In low-side, you don't have much common mode so CMRR is not that important, and input voltage is close to ground, so you don't need an amp that can take inputs beyond the rails.