The way I use Twitter is to download tweets to a local database, including images/videos/unshortened URL and then I view the data in my own UI from local DB.

It circumvents the tweet/account removals done by users or Twitter. Also I can do any kind of search/data processing I want.

I guess I'm not alone. You can't hide your data once they are made public.

It's interesting what is possible once you start treating web services as a data source. Sometimes there is much more exposed than is visible or easily consumable on the page and you can filter/search/consume the way you want without all the clutter/feeding algorithms around the original page/service.