In theory: yes. But actually: it would only be yet another push towards big ships. We already have enough of those.
Due to the 4 experimental weapons limit, medium ships at least also are a a viable option for AX use. If a bigger ship won't really give you more firepower, the other aspects of the ship can become more important. So while the limit of four seems arbitrary, it helps in having a bigger variety of ships being reasonably choices for AX duty.
Thus i think that actually a different implementation actually would've been better: a maximum of ONE AX weapon and ONE AX launcher. To compensate for that, a single one of these weapons would have to to four times the damage it does now. And they should also exist in small size. That way all ships but the hauler would be potential choices for AX duty. Of course, different factors would still apply, not all ships would be good choices, but the possible variety would be higher.
But alas, that boat has sailed. FD won't go ahead and remove AX weapons from already outfitted ships, so this won't happen. I can only theorize that it would've given us more options for AX duty. In contrast, due to the high influence of firepower, the suggestion which is once again repeated here would work the opposite way and would shoehorn AX oriented players into a smaller variety of ships. So i understand why people would want it, but i think it would not be in the best interest of the game.