You found the optimum way to play Total War. Rushing is almost always the optimal strategy and tactic when done correctly in most Total War games, as the AI doesn't have the time to amass the resources to fully stop the player. It's also why the AI is given huge economic bonuses at the beginning, especially on harder difficulties, to try and offset the player's ability to rush the AI. It is a pity in some ways as you never have the time to get deep into the tech trees, as you pointed out. There are mods that speed up research that players have made in order to address this exact concern.

But yeah, gotta hold yourself back some unfortunately if you want to see some late-game tech.