ISPs may have control over modems, but only their own devices that they ship to you. This means that in theory they can control whether that modem has particular WiFi capabilities, if it has a built-in WiFi access point (many modems don't).* WiFi setup is not the main purpose of that control plane though; the ISP needs to perform checks against the modem in case of connection issues, send firmware updates etc. TR-069 is an example of a protocol that can be used to remote-configure customer equipment.
If you are using your own modem, the ISP will not be able to control it. This has its benefits and drawbacks. In many cases, you may not get any kind of customer support, since the ISP will claim any connection problem to be caused by your own equipment. This is the reason why some ISPs do not allow third-party modems to be used, which they may be able to prevent from registering on their service.
But let's assume you're using the ISP's modem and they can theoretically control it. Even then, they won't be able to interfere with your local WiFi access. Since you have your own WiFi router plugged into the LAN port of the modem, and you're using that router to provide WiFi access, it's separated from the control plane of the modem, and it's nothing the ISP can influence.**
The $5 has nothing to do with providing any capabilities whatsoever. If you're not using their equipment, you shouldn't have to pay that fee.
* With respect to WiFi, well, there are special features that could be enabled. For example, where I live, one ISP offers a special type of guest WiFi that can be used by any customer of the ISP, even if they don't know my personal WiFi password. This means I can travel around the country and use other people's Internet connection through that special WiFi.
** The ISP will not be able to influence anything downstream since AFAIK there are no control protocols to do so. To the ISP, even if they could get a list of the devices connected to the modem (which they probably could), they would not be able to prevent your own WiFi access point from providing WiFi signal.