Because wireless cameras connect directly to the internet and offer remote access they can be hacked, putting your privacy and security at risk.
If you're using a camera that records to the cloud, then it will require the internet to function. However, if your cameras can record to an SD card, hard drive, or local network storage, then they should be able to function even if they're not connected to the internet.
Do all home security cameras require Wi-Fi? Not all home security cameras require Wi-Fi. Some cameras, like the Arlo Go and the Reolink Go, can use LTE plans instead of Wi-Fi. Other home security cameras aren't connected to the internet at all but rather record onto local storage like hard drives.
There are a few security cameras that work without WiFi. One option is to use a security camera that relies on 4G cellular service. Another option is to use a security camera that plugs into an Ethernet port (PoE) and records footage to a Network Video Recorder (NVR). 4G cellular cameras are your best choice.