Hello Juan
To establish the tunnel between LWAP and WLC, all you need is the IP address because the CAPWAP tunnel is created over the underlay network infrastructure that exists between the WLC and LWAP. As long as those two can reach each other, the CAPWAP tunnel can be established.
Why do we need all VLANs between WLC and the core? Well, it depends upon where you are performing your routing. If the routing takes place at the core network, then this must be done in order for the clients connected to each SSID to reach the default gateway of each VLAN. The default gateway will actually exist within the core itself. However, you can change that topology and make the WLC itself the default route for every VLAN/SSID. In that case, you wouldn’t need a trunk between the WLC and the core network. The scenario you described in your post assumes routing takes place in the WLC.
The question is, what is considered best practice in this? Well, typically we don’t want to overburden the WLC with routing, especially in a large network where it would have to act as router to all wireless clients. If the WLC has to handle, say, 50 or 60 clients, then you should be OK with routing at the WLC. However, if you have a network with thousands of wireless clients, it is best to leave routing to a different device, and this is why you need the trunk. That way the WLC will only be burdened with the management of the LWAPs and not routing as well.
Creating a trunk and performing routing on the core network is considered best practice, even in smaller networks. Does that make sense?
I hope this has been helpful!
Laz