It is not so much a management fashion as a recognition that organizational decisions (not-for-profit, private firms, public firms, governmental organizations) impact beyond the walls of the organization and that external actors (stakeholders) who are impacted by those decisions react--good, bad, indifferent--but their reactions can limit organizational discretion and flexibility-hence the concern with stakeholders.
Well, it is the fact that there were two schools of thought Freidman would always say the business of business is business ... and the business needs to bring in profit for the stockholders... comes Freeman and says, the stakeholders rather than the stockholders whom the business has to take care of!
Well, we have witnessed the damage that some businesses have done to the environment, and the societies through their concentration and fixation with profit... though, I will never say that we should not seek profit as businesses, but this should be part of the overall goals of the organisation... and not the only goal where the ends justify the means philosophy being applied.
I think that the "fuss about stakeholders" is not so much a fashion - but a discursive shift. Concepts that imply a clearer power relation (such as class, elite, pressure group or local population) are replaced by a concept taken out of a business jargon. While this means a "more" of possible critique towards the practices of given businesses, it means a "less" of critique of overall power relations in society.
I agree with you the fact the stakeholders were always there. However, now there is a paradigm shift. You want to involve in the decision-making processes by engage them, get their input to get a winning solution while addressing their demands and expectations. Before it was - my way or highway. Now, you want to see your stakeholders are actually contributing to the success of the project by creating a win-win situation.