Earlier today I discovered that you can get Tier Clearance from the Hall of Heroes just by meeting the gear requirements. I'm not sure if this is intended, as there is no mail or even achievement notification of this, when you acquire the Tier Clearance. You do get the Achievement upon logging in again, but not when you actually get the clearance itself. It seemed bugged and if this is intentional, makes entering the Clockworks before you get T3 clearance entirely redundant (except to farm for crowns but you can do that from missions and get additional Tokens). As I was able to get clearance to T2 by just doing the missions and then using the mist tank to continue doing the missions until you reach the Hall of Heroes, which only takes about 45 minutes. If you have received a gifted energy pack at the start of playing or have bought energy before playing, you could easily get Tier 3 access using the Hall of Heroes and missions in a day, including 4-star gear.
I'd also like to note that if you don't have a minimum of 10 energy, you cannot enter the Hall of Heroes even though it does not cost any energy to enter, this is slightly annoying.
That seems pretty on purpose to me, the mission description even says something about gaining clearance through the Hall of Heroes. And from what I understand, simple delving in the arcade won't unlock new tiers anymore.
As for the T1 and T2 arcade being redundant, I think that's just a balance issue. I would venture to guess that missions will be patched to become unrepeatable, or the Arcade will become more profitable than mission runs. At the moment, the Arcade is still the only way to acquire some recipes, though to both relief (I can finally get the recipes I want XD) and dismay (I liked the excuse to do random runs to look for recipes). the Hall of Heroes really does try hard to push Basil into the Obsolete pile.
As far as buying energy making the progress go a whole a lot faster, that seems like it would be obvious as well. Even before the Hall of Heroes/Mission System update, if you bought energy, making 4* gear right off the bat isn't difficult; though I will admit the mission system makes it go a little faster as they pretty much hand you your first set. (and if you don't like it, you can easily go to the mission lobbies or HoH to get the recipes you desire).
Essentially, the game went from "here's the basics, go knock yourself out" to "hold my hand". Not really a bug, more like a change in the game's design.