I think their main concern is probably people downloading torrents and anything of that nature. People who host free wifi hotspots should create proxies to avoid that problem. I think they should allow people to continue to tap into free wi-fi.
Not clear who "their" refers to. The concern of the FCC is that 1) (licensed wireless) broadband providers will favor some sources over others, based upon their content, but pretend that they are doing it in the name of efficiency, or that 2) they will charge customers different rates for the same level of service. They are also concerned that 3) the carriers will discriminate against applications that compete with applications where they, the carriers, compete.
For example, AT&T entered into an agreement (in restraint of trade) with Apple to forbid certain applications (e.g., streaming video, VoIP, and PC tethering) access to the cellular network. These are all applications that compete with offerings of AT&T on which, presumably, AT&T's share of the revenue and profits is higher. To the extent that AT&T would comment at all, they pretended that the issue was "protecting the customer from a bad experience," not to say, protecting an already fragile network from overload.
(It is interesting that AT&T permitted these applications on other phones. They seemed to be blaming the success of the iPhone for the problems of their network while gaining new customers, revenue, and market share.)
Both Apple and AT&T denied that there was any such agreement until the FCC began to ask questions. Then, without ever admitting the existence of such an agreement, AT&T gave a wink and a nod and Apple changed its position.
While one might argue that such behavior is already
de facto illegal, the carriers do not want it to be clear.
On the other hand, the carriers have a legitimate fear that regulations, adopted in the name of net neutrality, might, intentionally or otherwise, interfere with their legitimate right to manage traffic, or force them to invest more and more to maintain service levels at lower and lower prices. For example, at the same time that AT&T is investing in cells in Vermont where they have no customers but the cost is low, while not investing in San Francisco where they have lots of customers but the cost is high. Each new customer in Vermont is at least marginally more profitable than one in SF.
AT&T would argue that they should be permitted to make such decisions without interference from regulators. They would argue that the market is a better mechanism for allocating their limited resources than the regulators. While markets are often inefficient in the short run, they tend to efficiency in the long run. While well-intentioned regulation may produce desirable results in the short run, they tend to have unintended consequences in the long run.
This is a very complicated issue with good arguments on both sides. The FCC has claimed that their decision will be based on the facts. However, historically such decisions have have tended to be ideological, not to say political. It is not an accident that the democrats on the commission prefer the populist arguments while the republicans side with the market, not to say, the carriers.