Actually it sends copies of the food (one copy per connected city) and growing town specifically says "increased growth", not just growth. Actually everything in the interface suggests it should continue growing, but maybe it's just interface not reflecting some changes.
I read it as unambiguously saying that specialization stops growth. The +50% growth is similar to all other growth bonuses, and it is applied to growing towns. It makes sense when you want a non-farming town to grow to grab a resource, without feeling like you are missing out on all bonuses of specialization.
I feel like longer ages and standard ages are almost two separate games, and that mechanics are pretty well balanced for standard games. I am currently playing modded at halfway between.
Along with comments about this not working with any real AI pressure, I think what is missed in “all cities all the time” is that there are many opportunity costs to putting all gold toward cities for a benefit that arises much later in the game (with the camels/gypsum being needed to offset this).
-Gold can speed up your existing cities, which will then also produce more the entire game. At higher difficulties you need fast culture to compete for wonders, not more culture later.
-Gold allows you to field an army and purchase buildings while producing wonders, which make specialists in core cities more valuable than having many more specialists in immature cities.
-Moving all production resources to smaller towns will cause you to lose wonder production races at higher difficulties.
-Mid-production cities in early explo/modern feel really slow, struggling to build half the infrastructure I have tech for, when what I need are a few cities that can get important stuff up fast.
Also, in a standard age length game it is non-trivial to secure the treasure fleet golden age and towns with a bunch of obsolete builds are often unhappy and have low yields even in science and culture. There is no way it is optimal to convert a bunch of cities in Modern, unless maybe going to science victory. All as early as possible, you need gold for explorers, gold and about 6-8 cities for factories, and everything but cities for military.