My main worry about Rust dependencies is not so much the number, it's that it's still a fairly young ecosystem that hasn't stabilized yet, packages come and go fairly quickly even for relatively basic features. For instance for a long time lazy_static (which is one of the dependencies listed here) was the de-facto standard way of dealing with global data that needed an initializer. Apparently things are changing though, I've seen many people recommend once_cell over it (I haven't had the opportunity to try it yet).
Things like tokio are also moving pretty fast, I wouldn't be surprised if something else took over in the not-so-far future.
It's like that even for basic things: a couple of years ago for command line parsing in an app I used "argparse". It did the job. Last week I had to implement argument parsing for a new app, at first I thought about copy/pasting my previous code, but I went on crates.io and noticed that argparse hadn't been updated in 2years and apparently the "go to" argument parsing lib was now "clap". So I used clap instead. Will it still be used and maintained two years from now? Who knows.
Some parts of the ecosystem are more stable than others. That's true. And it takes work to know which things are stable and which aren't.
And yet, some things just take a longer time to improve. lazy_static has been stable and unchanged for a very long time and it works just fine. You don't need to switch to once_cell if you don't want to. lazy_static isn't going anywhere. The real change here, I think, is that we're hoping to get a portion of once_cell into std so that you don't need a dependency at all for it.
The async ecosystem is definitely moving more quickly because it just hasn't had that much time to stabilize. If you're using async in Rust right now then you're probably an early adopter and you'll want to make sure you're okay with the costs that come with that.
I guess what I'm saying is that it's an other problem with the current package ecosystem: you often end up finding multiple packages purporting to do what you need, and it can be tricky to figure out which one you want. As an example, if you want a simple logging backend the log crate currently lists 6 possibilities: https://crates.io/crates/log
I picked "simple_logger" basically at random.
