I am having this same issue in 2020. The shape I'm drawing always comes up with a gradient applied that is partially transparent (I had been working with that look intentionally at one point in this document). I want a solid shape - no gradient is applied, it says it's at 100% opacity, but I cannot draw a new solid shape! I restarted InDesign, checked every place I know of where this could be set. I assume I'm missing a setting but not sure what it could be.

I find this ridiculous - I use both Illustrator and Photoshop for years. Although even between them it is different I still could figure out how to do it there. But no chance on InDesign. Why, Adobe, doesn't it work exactly the same in all three apps???? C'mon!

Interesting discussion!   Ignoring for the time being the issue of whether or not EPS is an “obsolete” file format or not, some issues to consider: (1)  PostScript (and therefore EPS, Encapsulated PostScript) absolutely does not support transparency in any way whatsoever. You can hack around with overprint, but that really isn't the same as the 16 blend modes of the PDF imaging model. (2)  Although PostScript language level 3 does support “live gradients,” it doesn't support them in conjunction with transparency. (3)  PostScript does not support ICC color management. It is best at DeviceGray, DeviceCMYK, and DeviceRGB. Yes, there is such a beast as PostScript Color Management but it is not ICC color management and inconstently implemented; don't go there! (4)  The OP stated that with regard to this EPS artwork, “it's supposed to be used for both print and digital showing.” Well, unless you know exactly which CMYK is going to be used for printing, EPS can be problematic for 21st century printing which is overwhelmingly PDF-centric with ICC color management. And for “display” which I assume might be for web pages, EPS is fairly useless since no web browser supports EPS. EPS content would need to be converted to something else for direct web display, perhaps SVG? In any case, with several generations of lossiness due to conversions, quality is potentially going to suffer tremendously. (5)  Bevi gave some interesting examples of EPS issues. However, be aware that placing EPS into Microsoft Office formats yields only a raster bitmap unless printing to a PostScript printer (and even then, Microsoft no longer officially claims EPS support). (6)  If the content is for placement into Illustrator or InDesign, EPS is ridiculous since it is lossy per above. You want PDF for this purpose (even for logos and “simple” graphics (and by the way, when you allegedly place .AI Illustrator files into InDesign, you are really placing the PDF aspect of such files, not the actual Illustrator content – I strongly recommend that you save a copy of an Illustrator file as a PDF/X-4 from Illustrator with no downsampling of images and use of a lossless compression and place that into InDesign). OK, that all being said, I'll tell you what I really think. Yes, EPS is a wonderful late 20th century file format. We continue to support placement of EPS into Adobe graphic arts applications simply because there is so much legacy content from the mid-1980s through the first few years of this century in that format. We continue to support creation of EPS from our applications primarily due to the need to support Luddites who either stopped keeping current 15 years ago or more or who have coal powered, steam driven equipment and workflow software that can't deal with anything newer than PostScript-based technologies.                 - Dov

Like most things in Illustrator, you have to do 2-3 steps, vs InDesign where you can do it in 1 step (natively).When I have to work in Illustrator, I typically just do the gradation in PS, then bring it into AI as a PNG.

Meg The Dog's answer would work. Another way to do this is to create a rectangle in an essential graphic with a gradient fill.In the File/Edit menu at the top of the screen click Graphics > New Layer > Rectangle. Adjust the Rectangle size in your program monitor with the blue dots on the corners. In the Essential graphics window (Window > Essential Graphics if it isn't already open) click the Edit tab, then click Shape 01. Scroll down and click the grey box next to fill.In the Color Picker box that pops up change from Solid to Linear Gradient. Click the arrows in the gradient bar to change the color, the arrows on top are the opacity level and the arrows on the bottom are the color. For your question you will want to make both the bottom arrows black and make one of the top arrows 100% and on 0%.If you want to add more colors or opacity levels in between the arrows just click an empty space between them.