It absolutely does inhibit one's fun if there aren't any small housing plots available to own.
Again, the problem with your proposed solution is that it's only a fix for those players who are just interested in the gameplay elements (i.e chocobo raising, gardening) tied to housing. It does absolutely nothing for the players who simply enjoy owning, decorating, and having fun with virtual homes. And I think you're sorely underestimating how many players the latter applies to. It's one of the reasons housing is such a popular request in MMO gaming (where elements like chocobo raising and gardening don't necessarily exist).
Meanwhile, more housing (a lot more) fixes the problem for everyone - both the people who want to play house, and the people who want to garden and/or train chocobos. That is where the focus should be, not band-aid solutions that only cover part of the problem.
I'd even argue that moving chocobo raising and gardening away from housing will make the housing districts more of a ghost town than they already are (which is an odd problem to have considering the lack of free plots). The developers should be looking into a way to bring more life into the various neighborhoods, not add reasons for people to go elsewhere. I do agree that new "must-have" features shouldn't be added to housing until the problem is fixed. But, if anything, that should equate to lighting some fires under the behinds of some problem solvers rather than never expanding on housing features from here forward.
I'm not sure why the developers aren't choosing to expand the housing. I've not seen them come out and state "server costs" as the issue. The impression I've gotten is that there is still housing available on less populated servers and they're attempting to avoid spreading everyone out too thinly, that they don't won't homes sitting in the middle of divisions filled with empty plots. I can understand and sympathize with that, but at the same time there are more populated servers out there where small housing isn't available. And advising players to transfer servers isn't a reasonable suggestion. Many people are where they are for a reason.
Threads like this one aren't going to stop as long as the developers are making statements about being satisfied with the amount of housing available, as obviously the players aren't satisfied (and for legitimate reasons). It would help if the developers were more open/honest about what precisely the problem is. Useful communication would go a long way here.