The white house mail room will anyway do the final sorting to individual congressman, and this way you don't have to pay postage on each letter.
But still individual envelopes though (inside the box).
In the wikipedia article Canada and New Zealand are listed as having free mail to an official. Although it doesn't seem to be a comprehensive list, I don't think it's very common.
Also, it's much more impressive to have a barrage of letters to each congressman, rather than a bulk folder that contains all the letters to that congressman.
But maybe they don't have a centralized mail room? I didn't actually check.
The people working in the congressman's office are the ones who actually have the working relationships with the elected officials (to the point where they can sometimes pressure them if they think that constituents are feeling a certain way, based on calls/letters).