Net neutrality does not preclude metered access. Two different things.
There is a scarce resource, consumer bandwidth. We normally use pricing to communicate information about scarce resources. This has the advantage of increasing the profitability of investment in increasing the supply of the scarce resource.
The explosion in growth in streaming HD video services has meant that the statistical variance of consumer bandwidth consumption from mean consumption has increased.
If most pricing models assume a mean usage, that means that heavy users are now being subsidized more than before by light users.
For fairness, heavy users should be charged more.
That can be done via metered access with higher allowances costing more, or it can be done by charging more for the streams of data that are consuming the scarce resource. That means Netflix and their ilk. But of course Netflix will pass on any extra cost on to the customer.
These are two sides of the same coin. If metered access with segmented pricing can't solve the pricing problem, then contracts with suppliers of data streams will be used instead.
The more packets that flow through a congested hop, the more that flow should be charged (whether to the sender or recipient). Peering with a network where the packets are not due to go through heavily contended routes shouldn't be a big problem, and nor should peering with a network where the routes for packets being interchanged have similar constraints.
Probably, a totally fair system would involve so much accounting that most of the cost would be dominated by it.
Let's not also forget that Netflix et al. don't always rely on peering. They can give their customers a better experience by directly attaching hardware to the ISP's network, i.e. edge caching, which itself involves contracts and negotiation, independent of any network neutrality concerns around packets swapped at peering.
First of all, most big ISPs are competitors to Netflix. Directly so through online streaming services, but I think focusing on those is missing the big picture, which is cord-cutting. For cord-cutters, Netflix and other services add up to a replacement for the ISP's expensive TV service, and while not a lot of people do this today, the trend over the last few years seems pretty clear. Thus the ISPs have little reason to be particularly invested in general in making high bandwidth transfers on the Internet actually work.
Aside from that, they could be incentivized by competition from other ISPs. But 75% of American homes have only one ISP providing at least 25/3 [1], and even at 4/1 the majority only have two choices, so this is pretty limited. While I am very far from an expert in this field and I know there are many factors involved, it's hard to see this as not a large factor in the high prices Americans pay for Internet service compared to other countries, independently of the inherent scarcity of the resource (which, after all, can be expanded with enough investment).
And when it comes to charging content providers, the situation is worse, because the cost is hidden. Even in a competitive market for ISPs, fees charged to Netflix don't affect the sticker price - admittedly, at the moment it seems to be all of $1, which is a significant part of Netflix's price but not the Internet connection's [2], but that just reinforces the arbitrariness of it. And if negotiations fail and the ISPs slow down Netflix connections by neglecting to upgrade equipment, they can still advertise 100Mbps or whatever on their website, regardless of the fact that on one of the most popular destinations (bandwidth-wise) on the Internet you can't even get 5Mbps! This is such an enormous asterisk to the speed promise that even given the inherent variability of speeds on the Internet, it feels very much like false advertising.
This used to affect me personally: being in the minority that has two high-speed options, somewhat less than a year ago I switched my home's Internet connection from Optimum Online, cable service which AFAIK is not trying to charge Netflix a fee, to FiOS. For the same price it promised faster download (150 vs 100), much faster upload (now symmetrical, yay), and there were faster options potentially available in the future if we were willing to pay even more money. As it turned out, for most of the internet FiOS really was better - even if I could rarely ever download anywhere near 20 MB/s, 10 wasn't out of the question for CDNed content, significantly better than the previous service. But the result was to the significant displeasure of my family, because instead of downloading games from Steam, they watch Netflix a lot, and it started frequently degrading quality or failing altogether. As someone aware of the issue I honestly should have know that would happen... IIRC, since the connection was far from perfect under the old ISP I thought it wouldn't make that much difference, but I was wrong. My fault - I think largely resolved now that Netflix is paying up - but the vast majority of consumers are completely unaware of this! Any non-tech-enthusiasts choosing service during the time had little way of knowing about this giant caveat, giving Netflix no bargaining power even in this competitive segment of the market.
I suppose this part at least could potentially be changed without government intervention: Netflix could raise its price only for users of certain ISPs, or ISPs could start advertising their Netflix speeds. But with all these factors combined, the whole thing is a mess and in no way represents an efficient market. Thus while I hope for competition to some day make net neutrality-like regulation unnecessary, I strongly support such regulation.
[1] http://www.fcc.gov/document/fcc-chairman-more-competition-ne...
[2] http://arstechnica.com/business/2014/05/netflix-comes-throug...