You need to actually clear the payment with the payer/drawer's bank eventually. This means either having a direct relationship with all of the banks your customers might foreseeable use, or using a clearinghouse with pre-established relationships. One of the functions served by the payment networks (actually the merchant processors under their agreements with the acquirers I believe, it gets confusing in the details) is managing relationships with clearinghouses such as FedACH. These clearinghouses are hesitant to allow access to parties other than established financial institutions because of the risk involved, and they are likely to judge "starting our own payment network for adult content" as very high risk for a variety of reasons.
It is conceptually possible for an adult entertainment website to sidestep the payment processors by clearing directly through ACH or an EFT network or something, but this is high risk for the bank offering the service (ODFI) and so access to ACH clearing is generally more difficult to obtain than merchant banking. Banks are not really any more willing to work with adult entertainment than credit card networks, and some of the material problems that make credit card networks hesitant (unusually high levels of chargebacks and use of stolen card information) are even bigger problems for ACH/EFT/etc. which are "less reversible" than credit card payments.
The ease of processing credit cards today is sort of a newer invention - you used to have to fill out an application and usually meet with a banker for an interview to get approval to open a merchant account, because the bank that offers the account is taking on risk on your behalf. Newer processors like Square and Stripe have gotten rid of these requirements, but presumably incur more expense and use more automation in managing the risk than conventional banks (as a result they often charge higher fees than a merchant account at a good low-cost commercial bank).
A somewhat related example was the Federal Reserve's decision several years ago to not grant a master account to a Colorado-based credit union formed specifically for the cannabis industry---if memory serves, the primary concern the FRB identified was that the low diversification of such a financial institution would make it especially fragile in response to economic or regulatory changes, creating a very high risk of the credit union going insolvent if there was some shift in the cannabis industry. I imagine an FRB would raise the same concern in relation to adult entertainment, which is also in a complex and often unclear regulatory environment due to the history of US obscenity laws, the often cash-based nature of the industry, and much of the industry being overseas.