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It can be a board in each city like Market Board or it can be Social window like Player Search, this will make it easier to search for a FC to join, player can select the type of FC they are looking for, search and the board or window will show the FC meet the required player input and are recruiting player, and the player will be able to read the FC recruiting message and send applicant, this is another alt way to join and looking for a FC beside read on PF, or shout
I took to your idea at first..
But then there is reputation to consider.
If your reputation is that of a active Free Company, this FC search feature would not be needed, as you are there to represent and then recruit if you wish so. However if you're NOT active, as far as the community is concerned, you do not exist(Also I think after a certain time your FC house will also vanish. not sure about personal houses).
My opinion aside, this would be useful. It would be a good alternative to the typical "let's see what FC tags I see or recruiters I see shouting or using PF".
Same for Linkshells, I request a search for them as well.