This should come as no surprise. TWC, like all MSOs are in business to make money; with rising costs of operations and the huge overhead that was taken-on by upgrading most (if not all) areas to DOCSIS-3 (both at the Head End and at the user end) that cost needs to be offset... by charging a modem lease fee. TWC has been discarding DOCSIS-1 and DOCSIS-2 modems at an astounding rate and is only purchasing new DOCSIS-3 modems.
TWC customers pay STB lease fees and now there is a modem lease fee; unlike STBs, modems can be purchased to have the lease fee waived.
Regarding any service issues, for Customer-Owned modems, TWC will ensure that the downstream/upstream RF signal going to the modem is good and usable, beyond that is a customer-owned issue, just like customer-owned routers (the lease fee pays for support of troubleshooting/replacing the leased modem as Home Networking fees pay for support of wireless networking).
Regarding what modems are supported, TWC's corporate website has a list of supported modems and will likely support that their customers can purchase the same modems that they lease-out.
Regarding TWC's Digital Home Phone VoIP service, there is no fee for the use of a TWC-provided eMTA, however, TWC does not support customer-owned eMTAs for the use of VoIP service (all VoIP customers will be provided with eMTA free of charge).
TWC is a business, not public service, not a charity; TWC is in business to make money. Cable, Internet and Phone are premium luxury services and therefore to any business providing them, a premium fee is due, just like your cell phone.