I have a little "share" button on my iPhone that invokes Youtube-DL via Pythonista, so I can open any Youtube video and get a locally saved copy pretty much instantly. I can use VLC to stream YouTube videos without ads.
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.
Oh, and apparently there's a new contender too - Play.js includes a fully functional Node.js implementation with support for npm (via package.json dependencies). So now you can basically use any NPM package on iOS. I can already tell that I'm going to get a lot of mileage out of it :)
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!
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.