I presume that by "None of them allow skilling", you are referring to the fact that you can only contribute to citadel resources for your own clan.
"Visiting" another clan's citadel allows clans to have joint events at each other's citadels or allows members to invite friends or possible recruits to an event, such as a friendly war on the battlefield, or a joint meeting or party in the keep or one of the meeting rooms. Visiting other clan's citadels to see how they have theirs arranged and organized, can provide ideas for how to set up your clan's citadel.
"Guesting" is primarily for chat and communication purposes.
Many clans have formed alliances with other clans and being able to guest in each other's CC's makes it easier to plan and participate in joint events and keep up with what's happening in the other clan.
There are players that might enjoy the clan they are in, perhaps a PVM clan, but have friends that are in another clan that is more of a social clan. They can participate with both as a guest in the other clan.
Other players may not yet meet the requirements for a clan they wish to join, but are allowed to guest in the cc until they do meet the requirements for membership.
I think Tren has given an amazing answer. The only thing I'll add is the the whole point of contributing to one clans citadel is done for many reasons.
1) Stop being capping and jumping clans to help clans increase their citadel
2) Stops players training to 99 for free by hopping clans.
Out of curiosity why is it you wish to cap for other clans? Is it for money? for experience? to help? or something else?