Why would one player ever need more Army units in a battle than their opponent?

Question

I am learning the rules of Risk, but am failing to understand why, during a battle, one player would ever need more Army units than their opponent?

According to the rules of risk, during a battle each player compares their highest dice rolls. The player with the lowest roll of the two removes one unit from the battle. The players then compare their next highest rolls (if they have rolled more than die).

My misunderstanding can be explained in the following two scenarios I have created.

In both battles, the attacker rolls 2 die and the defender rolls 1.

Battle 1

In battle 1, the attacker has the highest roll and so the defender removes one of his units. Now the defender has no more dice and so there is no defending die to compare the attacker's 2nd die with. The attacker wins this battle.

Battle 2

In battle 2, the defender has the highest 1st roll and so the attacker removes one unit. As by the rules, the players should now compare their next highest dice. The defender does not have a next highest dice, only the one which they have already used in the battle. So what happens here? Am I right in thinking that once this stage is reached, the defender can reuse their die that have already won during this battle? And so 'Battle 2' would now look like:

Now, the defender wins again and so the attacker has lost all his units in the battle. The defender wins this battle.

Battle 3

Here is a 3rd scenario following the logic I have proposed:

Part 1:

Part 2:

Part 3:

Is this the correct process in which battles should be played?

Answer 1

I have since confirmed the rules. My scenarios for 'Battle 2' and 'Battle 3' are incorrect. Once a die has been used in a battle, it cannot be used in that battle again. The only reason for a player having more dice than their opponent is to increase their chance of rolling a higher number.

Answer 2

The rolls don't stay the same. Having more dice means you get more chances to outroll them, which is a necessity considering that defenders have an advantage.

Answer 3

The use for having more than one unit in a confrontation isn't for increased chances in the battle itself (as you stated in an answer), but for a more stable expansion after the battle. As I am sure you know, after a territory has been claimed, a chunk of the units in that battle move into the newly acquired territory up to leaving only one unit in the territory that you fought the enemy with. The problem with leaving token units behind and not fortifying them later is an unforeseen expansion into the heart of your territories. Let's say that you have a choke-point claimed that has a surplus of units defending from three separate forces. Because the forces are small enough to not be a major threat, you ignore that part of the board for a few turns and expand outwards elsewhere. Suddenly on the fourth turn, one force draws enough reinforcements to expel the other two from the entire chunk of territories leading up to your border and thus have control of all three territories that threaten the choke-point (providing 3 chances a turn to destroy that border with uncontested reinforcements from its surrounding territories). Since the fastest any unit can move is one territory a turn, if the bulk of your forces are on the other side of the board and your territories behind the wall are too soft, your opponent can take a huge chunk of your territories before you can bolster them.

TL:DR, It's so you aren't squishy later in the game