Check the ingredient costs, compared to the alchemy/enchantment costs listed in the Dragon Knight Saga FAQ/Guide
, to see if the battle tower platforms are upgraded.
However, you can also just use the corresponding functions from the NPCs in Aleroth (trainers in the ministry building, enchanter in the Phoenix Inn, etc).
If the shrine in the battle tower worked, you would be able to return to the previous regions in the game, which would mean they would have to change, and there is no point doing that much work if there is no game content there, etc. Also, storywise the siege of Aleroth is a little less dire if you can leave whenever you wish.
You are right that teleporting out of the Plane of Hypnerotomachia could break quest triggers, and the expected flow of the game. That could be blocked in other ways, but making the battle tower essentially a dead end (where you always return to the same location) is an easy fix, while still keeping access to the coffer, etc.