TLDR: Rust, Go and other modern languages don't use more dependencies than C/C++, but have larger binaries due to including libraries into the executable binary. This trade-off was chosen to ensure you can reliably run the executable on various systems without dependency issues.
I personally have gone with both options on several occasions. Being able to include an HTTP client without having to debug someone's cURL installation is certainly worth a few extra MiB's of disk space. However, I've also used C instead of Rust to avoid a very simple CLI program turning into several MiB's large binary (due to statically including the Rust std lib).