Thanks! For the second piece of feedback, I actually already do this for a few characters, like ム. ル is another good candidate. I am not sure if ウ is a bit of a stretch... Note this is also done for radicals with obvious correspondences, like 心草水獣, so you can search 水木 for 淋.

For the first piece of feedback, I have had other people request that, but I am not sure how to balance it with having detailed kanji pages. One thing to note is that while it is less convenient, on the detailed kanji page there is a link to "search this kanji" - I use that when I know a character that contains the part I want, but can't remember the name of the part itself.