To answer your question, Since ancient Phoenicians times, and Alexander the Great, archers, and later, soldiers with muskets/rifles were used to provide covering fire against defenders, keeping them away from the walls, or down below the top of the wall, so that they could not work to knock over ladders, before other attackers were able to scale the walls.
But, your vision is not very far off. Attacking forces expected to suffer 80 percent casualties on battle field attacks, right up through WWI. The Mexican army simply overwhelmed the defenders of the Alamo with their numbers, using the dark to get a huge number of men close enough to the walls before beginning their attack, that the smoothbore muskets were effective in shooting any defender who exposed himself over the walls.
If ONE defender managed to Not be injured or killed pushing over a ladder, there were 10 more ladders bring other Mexican soldiers up and over the walls. All the accounts from the survivors on both sides indicate that the final assault was accomplished very quickly, and with far fewer killed and wounded Mexican soldiers than had been anticipated.