I like terracotta pots. The added weight is helpful during windy weather for extra stability. I water nightly when it's needed, I have never had to water more than 1x/day. I think it is good that they lose water, that way I don't have to worry as much about excessive moisture retention or perched water.
When I store my trees in the garage in the winter and we get warm spells, I can take ice from the freezer and put it on top of the soil to help keep them cool and prevent early dormancy break, with terracotta there is far less worry about root rot due to excess water in the pot. With plastic I might run into problems during an extended or repeated warm spell(s).
It is important to shade the sides of the pot if the trees leaves are not shading it. Terracotta pots do build up heat and retain it well otherwise. However, this can also be looked at as a huge attribute. In the spring and fall when night time temps are cooler I encourage sun on the pots and take advantage of the retained heat and warming of the roots. Obviously, one must make sure it's just not too hot, so sometimes partial shading is the answer. Another bonus of fall pot warming is that it may help in the ripening process of your figs, especially with some of the varieties that require some heat to ripen well and develop better flavor. Depending on where you live you might be happy to get some warmth wherever you can get it. It's the same concept as removing the leaves from the lower portion of a tomato plant in the fall so the sun can warm the soil more and give you a bit more ripening before the freezes hit and your left with a ton of green tomato's on the vine.
This isn't saying that I am entirely against plastic pots though. The majority of my up-comers are in plastic. The whole constant up-potting process would be a pain with all terracotta for several reasons. A smaller pot also depletes it's water faster, so there is another plus for plastic. Ease of everything due lightweight is the biggest plus. As it stands, eventually my goal is to have all my big plants in terracotta, but I am trying some larger plastic pots too. I have to keep myself open to other advantages I may discover in the future, maybe they will just grow better.
The biggest reason that I am in favor of clay or terracotta pots is the organic or all natural standpoint, I don't want to worry about any breakdown or chemical leaching, period. Simple terracotta isn't painted with a sealer inside either(what is that stuff?). Glazed clay pots, maybe they are the answer for some people. Especially if you can not water daily.
I'm not trying to be a bummer, but there is one really big down side to those pots pictured in the beginning. You are going to have break them to get the root ball out when you chose to up-pot or re-pot.