Yes you can use any card you'd like to, and there are some out there with better than 2% rewards. It depends on how you want the rewards, cash back, travel, etc.
The advantage of using the Disney Visa for the down payment is the 6 months no interest for each charge. I believe the 2% reward with the Disney Visa requires the Premier Card, which does have an annual fee.
We will be using our Chase Sapphire Reserve card to purchase our next contract. We receive 3% on travel-related purchases. This card has a very high annual fee though. This is a good option if you travel a lot and collect points.
If you are looking for a low-cost interest-free method of paying, the Chase Freedom Unlimited is 1.5% on all purchases. There is also a new cardmember bonus of $200 (after spending $500) and interest-free payments for 15 months. This card has no fee.
We had a Disney Premier but downgraded when we got the Sapphire card. We just keep it for the on-property perks and discounts on ShopDisney.com