The information will probably not help decision making but replace decision making as players will have to deal with much less uncertainty.
Well, let me list some examples of why I think knowing deck contents allows for making interesting decisions. Of course, you can know these things without automated tracking, if you keep careful count. So then, why would anybody want automated tracking?
Think of it like a foot race vs a bike race. It's not fair for someone on foot to race vs someone on a bicycle, but within either race, it's fair because both competitors have access to the same equipment. Bike lovers are not somehow inferior or lazy because they use equipment to move faster. Similarly, although the advantage of automated tracking is smaller than a bike, it's possible to legitimately prefer playing with it or playing with it without being objectively wrong.
OK, on to the examples.
Ambassador war: I enjoy these more when I can know Copper and Estate counts to have some idea who is ahead at any moment. If you don't have a Silver yet, you may be aiming to have exactly 3 Copper in deck, so knowing how much Copper you currently have (and your opponent currently has, if they drop below 3 Copper) is useful.
Multi-Province turns: In a game without cost reduction and with a draw-your-deck engine, you'll typically want to aim for multi-Province turns. That requires a specific amount of buying power in your deck. For example, if your goal is to buy 2 Provinces per turn, you need $16. On a turn that you draw your whole deck, you can see how much buying power you have, but if you want to start planning how you'll get to $16 _before_ you first draw your whole deck, you need to know your deck's total current buying power.
Variable-value VP cards: Endgame decisions become more interesting when you know both how close you are to the next threshold and how close your opponent is. For example, take Gardens. If I see my opponent's deck size is 37, I may not be worried about them getting 4 point Gardens on their next turn, but if I see their deck size is 38, it's fairly likely. This allows for more accurate estimation of future point values. (I'll also mention Fairgrounds games with trashing, which I personally find incredibly annoying without knowing your deck contents, because you may unintentionally trash your last Copper and drop your point total.)
Balancing terminals and villages: Let's say you're running a draw-your-deck engine and want to end your turns with all action cards played and 0 actions remaining. Then you need n villages and n+1 terminals. (Terminal durations are interesting because they sort of count as half a terminal.) Planning this out becomes a lot more feasible if you know how many villages and terminals you currently have in your deck.
The unifying theme I think is that importance is shifted away from mental tracking and guesswork, and towards planning and calculation. This makes sense: when you have little information available, the most helpful thing is to gather more information and make decisions that work regardless of the unknown information; when you have a lot of information available, the most helpful thing is to make good use of it by planning farther ahead and calculating your turns more carefully.