PowerPoint meets all the bullet-points that were mentioned, but for sure it's not a 'pro' tool, it's just an easy-to-use tool (mostly!). I can't say if it is quick to use or not, because doing some stuff 'just right' will take time, depending on if one is a perfectionist or not. But if you don't make perfect the enemy of good, then PP can be very quick to create understandable diagrams of the type you showed. I'm just mentioning this in case PP had been written off as a viable option or not, that it might still be worth persevering with, if some of the features of it are unknown.
Going through the bullet-points that were mentioned:
* Regarding clipart/images, PP works nicely with Snagit. Clean up images (and remove background etc) with Snagit, and then paste into PP.
* Text can have outlines, shadow etc with PP
* Custom callouts can be created using the shape addition feature in PowerPoint. For instance, combine a rectangle with an arrow. The shape addition/subtraction etc is very empowering generally.
* Use the 'Curve' shape to draw lines approximately. Then, refine them using right-click and Edit Points. It takes a bit of practice but you can usually make it follow your preferred path almost entirely with this method.
Biggest downside is that the curve doesn't connect to other objects, so you could be tweaking often if the lines are placed too early in the entire diagram. As a result, I mostly rather use straight lines, or elbow connectors, since these will stretch elastically if connected objects are moved. Often you need the connector to attach at a different location on an object, and there are two ways to do that; (a) by right-clicking on the shape and select Edit Points and then add a point, or (b) [easier] draw a smaller simple object, like a triangle, with the apex at the location where you want the connector to join. Group the objects. Now connectors will attach to the apex. After you're sorted, send the triangles to the back, so they are not visible. That technique works very well for putting connections onto arbitrary parts of a photo for instance, and then send them to back after the connections have been made.
* Stripey insulation wires can be done by drawing a line or curve, giving it a thickness and a color, and then copy-paste it, and change the line style to dashed, change its color, and then drop it on top of the previous line. Admittedly not straightforward, but the result is good. This works with curved lines and the connector lines.
* The resolution from PP is excellent. There is some registry hack googleable to export at very high resolution PNG, but a simpler (lazier : ) approach is to just use a very high-res monitor, go to slideshow mode, and then use Snagit to capture the high-res output directly from the display, rather than an image export.
That technique that @Nominal Animal mentioned earlier about thin breaks where lines cross, is something I've found useful too, there's also a slight variation which is to use the 'glow' feature (with color chosen to be white) to give a usually invisible outline to some wires, which becomes visible at crossings.
If you look at the color diagrams that were in an earlier comment (before the long distraction of color-blindness) all those diagrams used many of the PP techniques just mentioned (for instance you can see a glow around a wire, use of connectors with hidden triangle apexes to anchor points, and there's also an example of where curved lines were made to join different parts of schematics, where the 'edit points' method was used to make it follow a path). Lots of copy/paste and the alignment and distribution tools within PP are great to speed things up. One other tip to speed up diagrams, is to keep all the 'best bits' in a single ppt file, for reuse. For instance, if you've already created handy callout boxes or particular overlays for photos etc., then you can use bits from that file as a template many times. I often do that with shapes that I created, like batteries, logic gates, even coiled wires of several colors! (since it can take a while to create that initially); it becomes a convenient palette of tech images/icons for your future requests that come up.
From my limited use of Visio, I get the feeling that it has a lot of flexibility too, and probably more powerful for diagramming, but I just happened to pick PowerPoint and got used to many of the features within it, that I now have trouble using Visio for anything but standard diagrams (e.g. flow charts etc).