Surfing the web makes only sense in portrait mode if you use the mobile version of the browser. Almost all standard websites are composed for horizontal viewing. The portrait mode might be useful for the iPhones and maybe the iPad mini, but especially the 12.9 iPP screams for horizontal usage (apart from reading magazines or PDFs...).
That's just way, way wrong. I'm a web developer and can say that nearly all content is based on vertical flow. You scroll up and down. Horizontal space is mainly used to allow for things like sidebars or more items in a row on a grid. Website optimization is done based on the horizontal width to make UI work for different size devices where the narrowest is a phone and the widest is that big 27+" desktop display where some silly person still uses a browser in full screen mode.
Having more vertical space generally gives you a better view of a website's information. When browsing the web I use my iPad Pro 12.9" most of the time in portrait orientation. On a desktop display my web browser usually is in a window roughly the size of the 12.9" iPad in landscape but with a much larger vertical height. For example viewing this page on a 12.9" iPad in portrait you can see roughly 4-5 posts in view while in landscape that drops down to about 3.