Well increased lean angle + throttle is the classic crash...leaving the parking lot, coming off a corner, etc. That ones' obvious to you, I know.
Yes, you can add lean angle and brake, but if it's done correctly, as you're adding lean angle, you're taking away brake lever into the corner as maximum braking has been performed straight up and down and we want to make sure not to overload the front tire at angle as well as get a little bit of suspension travel back in case there's a bump mid corner, etc. One of the bigger reasons for maintaing slight trail braking as you tip in is to keep pressure on the front contact patch. So yeah, it totally can be done, but usually a missed apex is a missed apex...gather it up, slow down and then turn back to it when comfortable.
It's why riding the street and maximizing an exit is a lot safer than maximizing an entry, IMO.