So there's one major flaw that was seemingly overlooked with the new BE system ...
I know there're a few threads on this topic already, and although they all hit home on the problem of low BE income with the new system, they don't address the biggest reason WHY this new system feels so bad.
I (regrettably) used all my newfound 25k BE in the essence emporium on various icons and ward skins since I couldn't afford anything more meaningful. And because of that, I won't be able to buy new Runes pages, champions, etc. until after some major grinding. Which brings me to the aforementioned oversight:
The large amounts of BE we received were supposed to be a REWARD for sticking with the old system. It was supposed to be a bonus. With how you can't even get BE without disenchanting a shard that you won't get until you play several games to level up, it feels a lot more like that reward was a prerequisite to be able to use/enjoy the new system. Perhaps Riot did actually take into consideration how much BE people would have now, but somehow they forgot about the fact that many will wipe themselves out with the essence shop that was meant for that exact purpose. The idea was there'd be an influx of BE and rewards since we don't need to buy runes anymore. Did they forget we still need to buy other things? I don't see a problem with re-implementing BE rewards per game.
TL;DR The bonus BE we got as a reward for using the old system feels more like a prerequisite to enjoy the new one, completely defeating the purpose of many aspects of the new system.