That's why the Tactical Style allows you to shift your place in the order
But once it is shifted, there is no benefit, unless you roll initiative every round (we used to, but decided to stop because of speed of play). Or maybe I am misunderstanding you? How about an example:
Round 1:
21 A
18 B
14 C
12 D
5 E
But D has the Tactical Style and INT 16, allowing a +3 to Initiative, so the order becomes
21 A
18 B
15 D
14 C
5 E
placing D before C.
Using the same initiative for each round (default in 5E), once applied the order remains for the rest of the encounter.
This gets back to my point about initiative in 5E. Supposing C was the enemy forces, once ABD all go, C goes, then E followed by ABD, then C. Repeats EABD, C, EABD, C, and so on. Everyone in the party goes (EABD) and then the DM (C). The repetitive cycle makes it so modifying initiative is only a benefit to D on the very first turn, after that, it really doesn't matter. Also, if D's bonus wasn't enough to bring it above C, it wouldn't benefit at all.
Do you see my point?
How about applying intelligence to AC at the cost of a bonus action. You could cap the bonus at your proficiency bonus. You can use your action to do the same for an ally that can see or hear you. If you have multiple attacks you can use one of these.
Not bad either, but I am focused more on using INT for attacking, preferably on the attack roll itself. However as others have pointed out, most combatants, if they lack high STR, tend to have high DEX, and will simply use DEX-based weapons.
However, your idea could work somehow as a feat as well.