I always assumed ‘high fantasy’ and ‘medieval’ were intertwined because it was a time when people were much more superstitious and didn’t have science to combat beliefs about how the world and gods worked. That and people were often inspired by D&D. LotR never struck me as all that medieval, nor did Lewis’s Narnia actually. LotR read like a tome found in the back of a monastery (which I’m pretty sure actually was the intention given the series exists in-universe as the Red Book of Westmarch if I remember rightly). Narnia meanwhile is a fantasy realm that exists in the closet of a home more modern than the 1400s.
In my own writing the time period may come across as medieval but I’ve mixed rather a lot of things into it. I love the (romanticized) medieval period (and the Renaissance) personally because everything was hand crafted and there was rampant symbolism and hidden meanings in almost everything. If you wore a dress dyed ‘true black’ you weren’t going to a funeral, you were quite wealthy. I chose the mainly medieval period for my story because I could dump in the many layers of symbolism and cultural significance into to world for the purposes of symbolism and foreshadowing and just creating a much richer world. I want it to feel real and lived in and as diverse as our own world.
"Remember, you go nowhere by accident. Wherever you go, God is sending you." - Rev. Peter R. Hale