I think it's a lowest common denominator thing. The idea that corporations are corrupting democracy is something that appeals to a very broad audience, and it's a political language that everyone speaks - it's one of the dominant memes in this generation's public narrative/dialogue. The disproportionate power of corporations over the political processes of representative democracy has deformed it in a very obvious and (if you're a fan of rep-dem) egregious way, that threatens the social class that's meant to be its bedrock - 'the middle class'. The Battle of Seattle, the tooing-and-frowing of campaign finance legislation, the Occupy movement and plenty of other things have solidified this meme's place at the forefront of the public political consciousness over the last couple of decades.
Focusing on the role of corporations in deforming the political power of 'the people' allows a massively diverse spectrum of people to speak a common language of criticism, and allows them to do that without having to involve/challenge the other aspects of capitalism that they might have a stake in (eg. property rights). Furthermore the specifics of this critical narrative means its participants to voice their grievances without feeling compelled to actually do much about them - corporations are faceless, impersonal engines, and so it's easy to resign your political agency because they can't be effectively confronted with the traditional, sanctioned forms of protest (but hey, what can be?).
As for getting people to expand their anti-capitalist horizons, that's a difficult question, and I think it depends very much on who you're trying to encourage, the locus of criticism has to be something directly relevant to their day-to-day lives. If you don't ground your criticism of capitalism in how it tangibly fucks with our individual shit then you just end up moralising, which turns people off. The idea that has resonated the most with my non-anarchist friends is that regardless of how much political power corporations have, work/employment is the same; we have so little control over the most basic aspects of our lives - what we do and how much time we spend doing it. Capitalism/democracy promises most that if they work hard enough they can forge a career in something fulfilling and enjoyable, and because that's not even remotely on the horizon of what's possible for my friends (and the vast majority of people), it's clear to them that capitalism is a terrifying waste of their irreplaceable time.
