Everyone in the organization should understand the importance of data and "steward" it accordingly. However, in the way I use Data Steward, it's an assignment that carries specific responsibilities to the data team. I don't want everyone to be one. I need the person or small group to turn to for what I need to build the data layer for that subject area.
I think everyone's a Data Steward from the standpoint that we should all be good stewards of the data, where "steward" is an actual English word. But, if you call everyone a Data Steward, it loses its meaning. I only use that title if a client really wants it. Otherwise, I'm in favour of building a data lifestyle and embedding stewardship tasks into people's everyday jobs.