Something Magic has that people complain about sometimes, that helps the issue a bit, is that Aggro decks naturally run less sources of mana. A refill card like Underbelly wouldn’t work in Magic because the aggro player would have to spend an entire turn, even late-game, playing it and maybe one other Murloc to trigger it once. It also means that aggro won’t always draw a creature/minion each turn in Magic; they will occasionally dead draw a land, giving a little bit of breathing room where Aggro can’t develop new options for a turn outside of what they had left in hand (if anything). Control draws more lands for turn than Aggro does, but they also run more cards that draw cards and more cards that use that mana.
Aggro, in Hearthstone, also gets helped by being favored by the aggressor in combat. But that’s just a matter of scale; the big problem is that aggro can play 5-mana worth of cards just as easily as Control can, so when Aggro gets a 2-drop that lets them spend 10 mana to refill the board late-game, that becomes pretty good. Magic has mana sink cards, too, but they aren’t playable in Aggro; they’re played in Midrange and Control.