Analog is movement, how often are you not pushing the stick in a brawler? In my limited experience attacking usually stops your character in these types of games anyway, you don't let go of the stick, you're always pushing it in the direction you want to hit.
The direction you're pressing, or none, while doing the basic combo changes it in Capcom beat'em ups and many others, and it's not trivial at all.
For example, in The Punisher:
No direction hold. Standard combo.
Holding forward. The combo ends with a dashing punch that advances your character forward.
Holding down: Frank ends the combo throwing forward the enemy he's attacking. It has invincibility frames. The enemy ends ahead of your character.
Holding up: Frank ends the combo throwing back the enemy he's attacking. It has invincibility frames. The enemy ends behind your character.
Position matter a lot in these games, because keeping all the enemies in one side is the way to avoid getting surrounded (and not get killed).
Similarily, holding a direction while attacking also changes your attack during a jump or when you have an enemy grabbed.
This isn't restricted to Capcom beat'em ups, either. For example, in Streets of Rage 4, two special attacks can be executed by pressing the special button, one wile holding a direction on the stick and the other without. Both get you out of hitstun, but only the one executed without holding the stick makes your character invincible. In the IGN SoR 4 gamescom video posted in a thread in this site a few days ago, the Axel player tries escape a combo from Shiva with a special, but he's holding a direction in the stick, so the special without invincibility comes out, so he gets hit again, losing extra health.
So, whenever I'm playing one of these games, "uuuh, I'm holding forward, so I'll keep it pressed because why not." is a situation that rarely happens.