Why is that?

There are a few reasons. First, contact positions or positions with an airbridge are more expensive due to more infrastructure. Also, for low-cost carriers, the ability to board using both doors of the plane is important to reduce boarding time, which is critical. For low-cost carriers, using a remote position allows boarding through both doors. In a contact position, you can only use the front door, which takes longer.

So, let's say I'm Ryanair and I'm asking for remote parking, but you, as the airport operator, are more incentivized to have me at a bridge. Who wins this battle?

The airport operator, always. The operator is in charge of managing the resources and the resource allocation process, so they have the final say in everything. For example, imagine you arrive at the airport, and all the contact positions are empty or most of them are empty. Then you arrive with a flight and are parked in a remote position. As a passenger, you might think, "What are the people from Aena doing? They're putting me in a remote parking position when the terminal is empty." There are reasons for that. For example, we might not know if the aircraft is going to leave early or not because the airline has not informed us. Imagine you are arriving at Alicante airport at 4 o'clock in the afternoon with an aircraft, and you see that you are parked in a remote position while all the gates and parking spots close to the terminal are empty. You might wonder why you're being parked in a remote position when everything is empty. The reason might be that, according to the allocation rules, if we don't know when the aircraft will depart, we automatically park all the aircraft in remote positions.