I think I wore almost exclusively wool/cashmere ties this winter - some blended with silk. I did wear sportcoats 95% of the time rather than suits. Linen silk blends are great for summer and I don't have enough of them.
I do like my silk ties blended with cotton. They give them heft and rigidity that I tend to like. Zegna tend to make lots of ties in cotton/silk blends and I must have at leat a dozen. Some only have 4-6% cotton but I love the 40% cotton ones. I have ties in silk/cotton weaves from almost all major tie makers. I also have some Pal Zileri corduroy ties in 90% cotton and 10% cashmere.
I have a 100% cotton madras (not patch) bow tie I keep meaning to put up for sale, and saw a similar 100% cotton madras necktie. I've seen other cotton neckties as well. Lisle cotton knit ties are also pretty common.
I have the same madras bow tie, bought from A&F 15 years ago.