atc98092
Not really the leased vs. owned router affecting the configurability. It is the custom firmware being installed on the particular router by the ISP. Currently, the leased Arris TG1682 and others should still be able to be user configured on Xfinity/Comcast. On Cox, this same router has been locked down, though.
Some Xfinity/Comcast leased routers are still user-configurable, some are not. Dependent on model number (which in turn determines version of firmware installed).
You are correct though regarding owned. As long as you purchase your own router, (and it does not have the ISP branding on it), it should be configurable. This is in contrast to CenturyLink routers. No matter where you buy those, if it says CenturyLink on the packaging, it will come with the CenturyLink firmware pre-installed.
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Bomber501
Normally, the ISP router is really both a Modem and a Router. Modem is for the internet. Router is for the network and organizing your connected devices. The preferred setting is that mentioned by atc98092. You leave the ISP router in place and set it to Bridge Mode. This means it will only act as a Modem. (your internet signals). You then connect your own router (usually via an ethernet cable) to the ISP router. Your new router now controls all your connected devices and and free to use whatever settings you want.
The ISP likes to control the settings because then they can manage all the bandwidth and speeds through their preferred settings to users. No matter how they try to market it, this is for their benefit, and not the end-user.
Personally, Bridge Mode of the ISP router, and using your own router is the way to go for most setups. However, you will need to learn a little about setting up a router and some ISPs are not very helpful to customers with their own equipment when an issue arises. FYI, setting up your own router is not very difficult.