There's a bunch of apps that let you load pretty much arbitrary code onto the platform - Pythonista and Scriptable are two of the top ones (Python and JS interpreters respectively), and with those you can do quite a lot.
It's not the same experience - that I'll grant you - but if you're moderately a power user iOS gives you enough to work with.
You need to install YouTube-DL via Pip, but happily the StaSh shell for Pythonista already includes Pip. If you're not using StaSh yet, give it a whirl - it includes a huge number of handy tools like SSH, Git, Pip, etc. Pythonista is awesome!