A few manufacturers are now shipping monitors with the same OS as their smart TVs, so they can stream Netflix and stuff standalone. OP has an LG one, and I know Samsung are also doing it on some of their newer models. Thankfully there's still plenty of dumb monitors on the market for now, including most LGs and Samsungs.
For now, yes. There also used to be plenty of dumb TVs on the market, but not anymore. If there isn't major consumer resistances to this (and let's be honest, most people already accept smart phones and smart TVs and smart cars and smart appliances all with the same shit) then in less than a decate you won't have many options for dumb monitors.
Given how garbage the software quality is on hardware devices, why would I ever want them to be connected to the internet? Ad/privacy or security concerns aside, even companies who should know better have shown they cannot be trusted and will continue to load up irrelevant patches onto a device until it eventually crawls under the increased computational demands. Slowing a previously responsive system.