Now that DawnBringer is becoming more prevalent in Arena (guilty as charged) I can see how people without it, especially beginning players who need the resources the most are really disadvantaged. The simplest solution would be give the Hero a random draft of a weapon that you own up to Epic rarity. However I propose that we have a tiered system of Arena based on early, mid and late game.
Early-game Arena (unlocked after first Quest): Keep it exactly the same as it exists with the exception of only using an Epic-rarity weapon or lower. Same buyin and rewards.
Mid-game Arena (unlocked after lvl 200?): the troop drafts could be Rare, Ultra-Rare and Epic, up to Legendary weapon for Hero. Hero class can be used and troops are ascended to initial rarity (16,17,18). Some troops are traited (3 for rare, 2 for UR, one for Epic) but no Kingdom Bonuses. Buy-in and rewards should reflect higher-tier.
End-Game Arena (unlocked at lvl 1000?): Can draft Epic, Legendary, Mythic troops, Hero has access to all Weapons available to them. All troops are fully leveled, ascended and traited. Maybe even make Kingdom Bonuses apply, though that might make it too-PvPish. Of course, buy-in and rewards should reflect end-game.
EDIT: Once mid and late-game Arena is unlocked you still have access to the other Arena modes so you can have the full experience