While it's great to work on a project from scratch UX is also applicable to existing apps and websites.
Honestly, wherever you find bad UX you can make a practice project from it.
If you're looking for something for your portfolio then the important thing is not necessarily what project you choose to work on but how you document your work. As long as you can demonstrate correct use of UX principles, a good understanding of the UX process, valid conclusions and wireframes or even mock-ups to demonstrate the end product of your work, then your portfolio will work.
You may even be able to go back and demonstrate these skills in projects you've completed in the past - Take a project where you feel you have demonstrated some UX skills/principals and write it up as a case study.
Bad UX is everywhere. Ever since I first starting working in UX (almost a decade ago) I have found myself frustrated by door handles, lift interfaces, automated checkouts, road layouts... the list goes on - plenty of material for projects.
I would suggest breaking things down so that you're not launching into an entire project - think about small projects: quantitative research, qualitative research, wire-framing, user journeys, rapid prototyping... do lots of short limited projects until you feel like you've got the hang of that particular task. One of my personal favourites is the 'OK' button: OSX places the 'OK button to the left of a row of buttons where Windows places it to the right. Which, if any, is correct and why? - You may even find your own personal preferences lead you to looking for particular roles.