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We already discussed the arguments for Hive and Hex above.
"In some games, you build the Town Hall on day 121, turn 4, while in others, you start building it on day 122 due to resource, gold, or army constraints. Also, don't forget about the availability of a hero for the Town Hall. If the difference is minimal, this leads to even richer games becoming even more unbalanced. In my opinion, the difference should still exist, even if not as significant as it is now."
Besides the probabilities in the game, there are many other random factors. For example, cities with a Town Hall on day 5 will become even more overpowered because each day of delay in construction in your version guarantees a delay in gaining control. Other Castles without nearby towns/villages with a Town Hall on day 5 will be forced to take a rest.
You are only considering one variable (and there are also the presence of elements, the number of resources, the number of convenient objects for the army, the length of roads, and the Castle with a Town Hall).
Added 7 minutes later
It's better not to grant control immediately after building the Town Hall because:
1) Town Hall level 4 is very easily built by gathering resources directly on the road.
2) With the current rebuilding mechanic, this will allow you to learn other spells; control doesn't solve all problems.
2-3 rebuilds are easily done by the middle of the second week; there is no delay in the game. If you grant Town Portal immediately, you simply won't have a use for it; it's just not enough, given the small number of cities. This will make games with excellent short roads even more important; if you manage to have, say, 5 cities on those roads by the time you get Town Portal on day 121-122.
And again, the influence of a fast Earth magic on the Mage. By the middle of the second week, at least someone will be using it, or the Warrior will be leveling up and using Earth magic, and Wisdom.