The lookupbar is associated with the window chrome (ie. there is one per window). Inserting it into the DOM requires emulating this behavior by synthesizing one "bar" in each tab, adding and deleting them at the right time, etc.
Inserted content always has the possibility of interacting poorly with the scripts and styles of the underlying page (or other extensions). Rikai-chan already has problems where its overlays will end of underneath page content.
Inserted content goes below the line of death (https://textslashplain.com/2017/01/14/the-line-of-death/). There are other minor deficiencies: you can't get the browser's theme on the bar, etc.
For Rikai-chan, it seems like it'd be nice to allow the background script to write to a page that sits on top of the space that shows the actual page and have the content scripts communicate what should be rendered. AFAIK, the only ways to show something on the screen is to either send it to the content scripts and have them modify the DOMs, or show it in a popup for a button.
[1] https://chrome.google.com/webstore/detail/rikaikun/jipdnfibh...
Rikaichan allows translation of Japanese words simply by hovering your mouse over. It works much better than entering words into an online dictionary, since nearly every free JE-EJ dictionary uses the same source, and if a conjugation isn't translatable it will cut the word off giving the meaning and then letting you easily highlight the conjugation to figure out the meaning of the two together. Its just much faster than using something like jisho.org if theres a lot of words in a text you don't know. Rikaisama makes Rikaichan even more powerful with a lot of extra features
Everytime I've ever tried the similar plug-ins on Chrome they've all been terrible, missing words, missing conjugation, or just being slow in general. Its the first check I do every time I think about switching browsers.
However with the new Electrolysis on Firefox its completely broken and it seems like the dev might not want to do a rewrite since the plugin works exactly how you would want it and has for a few years now, but especially not if the sandbox changes make the plugin impossible to work.