To be honest, Amsam is not entirely purpose-driven. It partly acts as a demo for some cross-platform development tools including nguigen. However, it aims to offer some image-cropping features that are not found in many image editors and viewers.
Amsam lets one quickly preview a photograph under different aspect ratios and make a crop. Despite being simple to compute, this is not easily done in feature-rich software. For example, you'll have to first open a calculator and manually find the new dimensions in order to do this in GIMP.
But that's not the whole point. The goal of Amsam is to be an "aspect ratio explorer", rather than just a cropper. It helps one review their compositional choices under popular aspect ratios. Generation of something similar to contact prints is also under consideration.
Not yet, but this is in the pipeline.
When one opens an image, the first thing any image editor does is decoding it and converting it to an internal representation. If cropping the image means manipulating this buffer and recompressing it, that results in unnecessary changes to the pixel values. It is possible to avoid this under certain conditions, and jpegtran does this (but it's a command-line program). Amsam is not fully there yet, but it's in the right direction.
With features like cropping-without-recompression in the set of goals, support for each format has to be implemented separately. JPEG is the first choice since that is the standard output format used by all kinds of cameras.
It's a fun practice followed by photographers to get everything "right" in-camera, including the composition and coverage. Chopping off the top and bottom (or the sides) could still be a requirement if the target aspect ratio is different from the one used by the camera (say to make it a wallpaper). This is more common in videography (see Letterboxing).
Preserving EXIF is certainly a goal, but it'll take time to implement. Verbatim copying of EXIF metadata isn't an option because it can lead to issues like the file having an outdated thumbnail (this particular issue may leak sensitive information as well).