I have to design sales agreements that only vary a little and it would be so much easier to do it with layer comps as opposed to multiple files or layers that are just copies of previous ones with small changes.

I desperately want this too. I often have to create multiple versions (5-6) of a 12-20 page mailer for different tiers of customers, where only a few pages have different copy/images and I have to name a few layers per versions to turn on and off for each version. Also, with the ability to export/package each "Layer Comp" versions as its own separate INDD file when they need to go to press.

It would be great if layers were either grouped, OR if you were able to appy a "Layer Comp." Both of these are like in PhotoShop. That way, with a couple clicks, I could switch between versions effortlessly.

Currently, besides the option of turning layers on and off, the only other option is to create a document for each version which means having to make the same corrections on the pages that are the same between each and is wasted effort.

I agree, I was about to request this feature myself. I work on big digital InDesign documents that have pop-ups on certain pages. I need to show those pages with and without the pop-ups when I create a PDF. Layer Comps are a life saver when working on jobs like this in Photoshop, but when done in InDesign I have to export 2 PDFs, one with the pop-ups layer hidden and one with the layer visible, then I have to manually merge the pages. This is a tedious thing to do, especially when making amends and resupplying a new PDF a few times in 1 day.

The only thing is, would Layer Comps work on a multi page document which is how I work in InDesign as opposed to when I work in Photoshop using a single canvas with folders for each page? Would Layer Comps only work if everything was on 1 page in InDesign and use a layer for each page?

agree. I have documents where all the pages are the same but the backpage has a different set of addresses and logos. I either have to create a different back page for each variation needed, or I need to add extra layers to put all the variable info on the same page.
I would like to be able to name each version and easily select a version to output to PDF without having to manually turn on one layer and turn another on, or change the page number to output each time.

Ideally, the feature would work similar to Custom Shows in PowerPoint (I can save a series of pages and give them a name) or Layer Comps in Photoshop (I can turn layers on and off and then save them so it's easy to pull up the next time I need to output that particular combination.)