I do leave a filter on every lens all the time. On the 100-400 and the 50 it's a UV filter, on the 24-105 it varies between UV and circular polarizing. I do have other filters for indoors use, such as one for fluorescent light.

I feel very uncomfortable leaving a lens exposed to the elements, knowing how much greasy dirt & dust gets deposited. After a day's shooting I take off whatever filter I was using and wash it in fresh warm water and mild detergent. You'd be amazed how much muck comes off it.

Although there are several UWA zooms available for cropped sensors, there aren't many for FF. There is a Sigma that I've considered, but given the profile of the front element it can't take a filter, and I don't think it would survive long in this environment.

Some lenses are quite intolerant of filters, and you have to be careful only to use one recommended by the lens manufacturer. Otherwise you can get auto-focusing problems and some vignetting.