I think I hit level 63 or 64 without a legendary champ, and the level cap used to be 60! This necro is old enough the game still capped you at 60 and had zero login rewards and no login champs.
Needing to play the game with predominantly rares at first, then with epics, working your way up to NM and then UNM Clan Boss? That's the way the game is. Many of us, including me, built our first NM top chest teams with only Rares and Epics, and our first UNM teams with perhaps a single legendary, if not just rares and epics.
Getting to Nightmare top chest, and pushing UNM? That is the engine from which collecting leggos is derived.