Total control is good for small charts and for especially important charts but for complex uses, the number of clicks and drags required to perfectly position connectors really rapidly degrades the editing experience, especially if you’re still working out the contents of what needs to be depicted.

As a result, for either high-speed or larger scale usage, my experience is that text (in combination with constraint-respecting automatic layout options that suit one’s personal aesthetic) really starts to shine.

Pro tools like Omnigraffle handle that sort of thing. Best of both worlds.

And omnigraffle can take a dot definition as input and the let you fiddle with it manually, it is really a joy to work with.

yEd is freeware (not free software) but I have not found a better program that matches accessibility (Java-based so runs cross-platform) and sophistication in automated graph layouts.

That's very true. On Flowchart Fun we have a bunch of layout algorithms you can choose from, but even then making a great-looking graph usually requires some manually tweaking like you said.

Have you found a tool similar to plantuml that runs completely in the browser? I could deploy the web server but it would be nicer if I didn’t have to maintain a running server for generating the images.

That's sort of what https://flowchart.fun is. Although, it doesn't have as many graph types as PlantUML. Mermaid also has https://mermaid.live/ running in the browser.