I've been starring the words with inadequate sentences so that I can later log into the website and pick better ones.

The best example is with 修正. The default example sentence was 我会 _____. Not very descriptive.

I had to log into the website, go into my starred words, and pick a better one. This would go so much faster if I could do this from within the app. I understand you don't want people inputting sentences, but choosing them from within the app? If it's not too complicated to add, it would be really useful.

It is fairly complicated to add, but it's definitely something we will consider, since it would be useful and it would help improve the sentences for everyone.

Loosely related, it would be awesome if we could "tag-star" in iOS so we can actually remember why we starred the word once we're back on desktop.
(obviously, many people use stars for words to study more, but for me, and seemingly others, it's just to flag words to check on the desktop)

+1 to nomad wolf. I would really find this a useful function

If you wanted to test out the tag-starring, could you star the word and then add a quick note in the custom definition or mnemonic?