And more importantly, because it is closed source and connects exclusively to Binance's servers to obtain transaction history, broadcast transaction, and so forth, then even if you don't end up losing your coins on it Binance can still harvest all your data and sell that to all the usual third parties and governments.

Typing "bitcoin wallet" or similar in to Google is one of the fastest ways to download malware and lose all your coins. You shouldn't be using Google for anything. The ads which are promoted at the top of every page and the first handful of results are more often than not complete scams.