So, there is no precise way to completely control the size. However, it is possible to control to a reasonable extent. That said, here are the things one can do.
- First is to import the icon into the folder and consistently use the same ones across workbooks.
- Second is to try your best to control and standardize the "size" slider in Shape Marks - within each sheet that you would be using - You have to be reasonably OCD to get this right.
- Third is, you can control the width manually once you drag the sheet in.
These are pretty much the only ways that I know. There could be others as well. With regards to published vs Desktop, it is definitely not a wysiwyg tool. But it would definitely be helpful when Tableau gets to "Pixel perfect" reporting space (in every aspect of the viz objects).
Controlling bar chart width is a big hassle right now. Some times, I am forced to keep a template chart and re-use them. So I get consistency in widths. Wish there was a number I could put in, and forget it. Like transparency.