That would make a lot of sense.

Not to spam or anything, but I'm going to copypasta my bump to the Linkshell Administration thread in UI - if Companies end up being the new linkshells, I would hope they incorporate more improvements upon the original XI design.
Additional rank levels - It'd be nice to have one or two more levels of granularity between "shellholder" and "sackholder". You might want to give some people the right to issue pearls but not to break them. Keeping with the "pearled" theme, you might move sackholder to the recruitment tier, and add in Pearlbinder and Pearlkeeper or the like. Further...
Moderated chat - Allows members of a specific rank or higher to "quiet" the channel so that they can speak to everyone without being interrupted. This is pretty important for larger-scale events. I'm sure everyone is familiar with the "STFU WE'RE IN DYNAMIS" type of situation. In moderated chat mode, if the original individual that set moderated chat logs off, the chatmode returns to normal (so as not to mute a shell for an indefinite period of time). If someone sets moderated and leaves it on without freeing it, players are free to /tell another officer asking them to disable it.
Rank list - Since it seems that XIV retains the linkshell member list while people are offline, it would be useful to be able to view the members of a particular rank at any given time, in case you need to contact an officer with a question or concern.
Transfer ownership - If LSes will have persistent space in XIV (see the Lodestone), then the LS itself should be able to persist through a player's departure. The owner should have the ability to hand the shell over to another player. OR...
Decentralized leadership - Perhaps the best solution to the idea of being unable to transfer a linkshell would be the ability for a shellholder to promote people into shellholders, allowing for multiple people to be fully "in charge". That way if a shellholder goes MIA, the linkshell does not have to dissolve. Some groups may be more oriented toward this style of leadership anyway.

Given the implementation of achievements and their integration into the Lodestone, and Linkshell integration into the Lodestone, I feel rather positive that there will also be Linkshell-oriented achievements coming, and so there may be a package of changes that will encompass some of these requests in the future.
To clarify on that last bit, WOW has guild achievements, so I wouldn't be surprised to see them make their way into XIV.