Hussar
Legend
I think AD&D does support a style of tactical combat. When I was trying to run 4e without mini's or a mat I still wanted to do tactical combats. I realized that I could do very similar things in AD&D or other games without a mat. It takes a lot more DM adjudication, handing out any possible to hit/damage bonuses, asking for appropriate ability checks and using much more detailed descriptions about what is in the area. In many cases players would naturally try and exploit the terrain.
For example I ran a Moldvay basic/expert game of the Isle of Dread recently and I would describe the jungle and the vines and some interesting terrain of fallen trees and torn up ground. My players would ask about and try things like climb upon the fallen trees or swing from vines or baseball slide under/into a copse of thorny bushes.
There is some hint that this kind of thing was intended, the AD&D players handbook example of play the thief slinks around the battlefield until they can get in position to backstab the illusionist. In Moldvay basic example of play the party arranges themselves into a battle formation to protect the spell casters.
I think much more detailed tactical play is possible.
Well there's the trick though. Since virtually none of that is actually covered in the mechanics, you're pretty much just making it up as you go along. And, yes, there is some tactical play in AD&D. Obviously you cannot remove tactics entirely. Just like you cannot remove the strategic/logistical level entirely either.
But, I don't think it's terribly controversial to say that one edition focuses more heavily on one aspect than another. The level of strategy involved in high level 3e play is such that it's not unreasonable to have spreadsheets to calculate your modifiers. Half a dozen different long term buff effects and you have a huge number of interactions. Particularly since a number of the buffs affect other buffs.
This is a level of strategic play that you just don't see in 4e. You typically can't since it's so difficult to pre-buff in 4e. And you typically don't see it in AD&D either since most of the buffs don't exist in the spell lists.
It's not that one element is absent in any edition. It's more that one element is more strongly focused on.