Simplifying Smartphone Browsing from a UI Perspective

I’ve been browsing the web on a smartphone for some time now- and a recurring issue I’ve had has only recently begun to bother me tremendously. I guess this means the honeymoon period is over. I had been willing to overlook poor design and dubious usability in exchange for the fun and convenience of mobile browsing, but as it has become a standard for me, I have begun to expect more. And for more and more users, this is going to be the case. I’m sure we’ve all seen the stats of how large the percentage of users browsing only on a phone or tablet has become- and as designers/developers and companies serving their content/products to the web, we need to become more sensitive to the idea that many out-of-the box solutions aren’t good enough anymore. Take as an example this site:
I visit this forum quite frequently in the ever-expanding pursuit of audio nerdery. I probably visit it from a phone 50% of the time. I’ll admit that I have an app that lets me browse it in phone-friendly format, but it also cuts out a lot of features and can be unreliable at times, so I still visit it in the phone browser pretty frequently. note this photo:

Even if I zoom in, it’s quite difficult to select a particular page from this tiny list of links- something that would never occur to a user(or developer) on a desktop.
Or take this e-commerce site as another example. it not only features the aforementioned(and quite standard) tiny links, but also has a giant row of banner ads placed perilously close to the menu. I won’t tell you how many different(wrong) pages I visited before getting where I wanted to be.

I pull these two examples as they are two products(forums and shopping carts) that quite often come with a lot of pre-determined styles, and a long history of “standards” in terms of design. There are multiple solutions one could consider to solve this problem, but I admittedly don’t even know what’s best at this point. But this problem, and many other similar problems, are the ones that we must face in the very near future as mobile browsing redefines the web landscape.