An ARAM only account is an account that only has the best champions for Howling Abyss in their champion pool. Mainly ranged champions with a lot of poke.
It increases their chances of getting a better champion, which also increases their chances of winning.
Besides free rotation champions, someone with an ARAM only account would have a roster like this:
{{champion:3}

Those are not all the strong champions, google ''ARAM tiers'' to see which tier each champion is in. The champions I listed are strong in ARAM, because they are ranged and have lots of poke.
Blitzcrank doesn't have poke, but his hook is what makes him so worthy. Galio doesn't either, but his ult is what makes him so worthy,
ARAM only accounts dominate the early game since they have champions with lots of poke, and champions with none, or melee champions won't fare well against full poke comps early game, but that doesn't mean a team with no poke can't win.
You can have a full tank team, and if you last long enough, you will outscale the opposing team at some point if they don't end the game soon.
ARAM isn't the most balanced mode, but ARAM only accounts throw the balance off since they only purchase the best champions and it kinda ruins the fun for others, since they may have a more diverse champion pool.