I am trying to understand why these curves are important, and what they are used for in the industry today (if not at all).
Benchmark yield curves: Make it easier for market participants to efficiently price interest rate products off such benchmark yield curves because there is a consensus and agreement on what serves as benchmark. Those could include government security yield curves, inflation adjusted/reflecting yield curves, among others.
Funding curve: Is a set of rates more specific to an operation rather than the whole market in aggregate. As every operation poses different risks, each operation hence also exhibits different rates, charged, to fund its operations. This can be the funding done by the treasury/finance department of a multinational corporation or it can be the funding costs of a trading desk pertaining to the funds extended to it by the bank internally.
Basis Spread curve: Is closely related to basis swaps in that 2 parties exchange 2 different floating rates and the basis, the spread between those two, can be visualized over all terms via a basis spread curve.