I'd like to see this implemented as well. William's link is quite nice and explains things I wasn't aware InDesign could do because of how cumbersome working with tables is; however, it fundamentally does not provide the exact functionality of a background image which would allow the cell to simultaneously contain text that isn't fighting with the image, anchor points, etc.

You can do some pretty interesting things with diagonal lines and custom stroke profiles, but that only gets you so far and it's not particularly intuitive either.

In my use case, I'm preparing a calendar with overlapping solar and lunar month numbers. When the month changes, I like to have a subtle indicator. Unfortunately, due to complexity, layering is pretty much the only means of coherently managing everything that goes into the calendar, but InDesign already slows down so much dealing with tables, I hate adding another one for something as subtle as a graphic backdrop.

I should also mention that I would prefer not having individually linked/embedded images because of the sheer madness if I needed to replace the graphic and updating potentially hundreds of links would be problematic, not that it's difficult, just disconcerting and error-prone. Having a single reference point in the cell style would be so much less of a hassle.

I had a file where I tried using table cell background images and had a lot of problems. It was a 4 page A4 document which listed a lot of e-learning and which countries it was available in. Those were full opacity flag images and where it wasn't available they were 10% opacity (so faded back). There were somewhere in the region of 2500-3500 images and it made the InDesign file pretty much unusable it was that slow. I spent some time experimenting with different image types and sizes. Illustrator vector files were the slowest and made the exported PDF absolutely huge. Even making the images tiny, and I'm talking 15 pixels wide still didn't make any difference. Changing the Display Performance setting to Typical Display or even Fast Display didn't change how slow it was. It did seem that having that many images in one file was too much for InDesign to handle.

In the end I did the table in Numbers then experimented with how wide all the columns needed to be to make it fit properly in the InDesign file. I then updated that each time (which was easy as the file supplied to me was an Excel document anyway), created a PDF from Numbers, opened that in Illustrator to get rid of the odd things that Numbers added and then importing that into InDesign with everything else needed and then exporting again as a PDF. Sounds like more of a pain than it actually was.

It's something we don't do any more but I thought I'd mention it in this thread.

Wow, thank you William I had no idea about this! This works exactly how I dreamed it would, and it changes my life!

I'm not sure which version of InDesign you are using, but as of 2015, this is a feature. See this help article: https://helpx.adobe.com/indesign/how-to/insert-image-table-cell.html