Each city level up is nice insofar as you get a free "perk" or building, but anything beyond that?
Well, in addition to the free improvement, you also get more cash/research/production. I am unsure of the precise numbers, but I guess this is a good thing to know. Checking...
Taxable income: 2, 6, 12, 24, 50
Research: 1, 2, 4, 8, 16
Production: 0, 2, 4, 8, 16
Seems to me that the "growth" buildings are a total waste of time, since you're capped by your total food, and you'll get there sooner or later even with just the default growth.
There's two kinds of growth buildings. Broadly, one kind increases food and the other increases growth. No need to explain why the first one is very important, as for the second...
Many strategies rely on having a lot of cities, and of course, the larger the map, the more cities you are likely to end up with. If your sovereign is not going up in levels, it is easy to come to a point where your level one cities are practically not growing, and thus not turning into specialized cities. Furthermore, you really want your towns, fortress and your conclaves to achieve high levels, because they have incredibly useful level-up improvements.
A level 3 town can add 10% to the health of every one of your units. At level 4, it can add 1 production per material to every one of your cities.
A level 3 fortress can add an awesome perk to every unit produced there. At level 4 in can generate free metal. At level 5, it can add more attack/health to units, or reduce unrest to the whole empire by 30% (which can mean hundreds of Gilden in taxes)
A level 3 conclave can add essence, or increase research while idling. At level 4, it can increase research everywhere by 10%.
It's because of these improvements that governors, growth enhancing buildings, outpost upgrades and enchantments are used. In my last game I had my main fortress at growth 11 - three consulates, the theater of wind, a governor, an enchantment (when not cranking out troops) and the head of an elemental lord.
As for food caps, once your empire gets going with a few towns, food caps are lifted. Enough grocers, bakeries, butchers and a brewery, and you will get 200+ food per grain. And if not, there's enchantments increasing grain and food-per-grain.
By the way, I am sure there's very nice improvements at level 5 for towns and conclaves. I just have not had them for a while, and do not want to give obsolete info.