Built-in autosave feature (for the TE version).

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1. Simultaneous turn is not applicable.

1. Or maybe in the first few days, while simultaneous turn is active, this option shouldn't be enabled, but rather, for example, to allow controlling neutrals after switching to turn-based mode? This would even be better in terms of NOT peeking at the starting army and the opponent's setup, so they wouldn't take restarts. And from the second week, you can already meet the opponent or assess the army through a few taverns, etc.

2. The game will become like a game with an open map.

2. Considering the answer to the first point, I think knowing the opponent's army from the second week won't be as critical, especially since the map itself remains hidden. In this regard, if strengthening secondary skills is planned, the scout skill could be enhanced by allowing viewing of the enemy camp. For example, a hero with the scout skill, if stationed in a city with a tavern, would replace the number of taverns with the scout skill level, or it could be tied to the hero's level, so that a level 10 hero with the scout skill is better than a level 3 hero.

3. Game time will increase.

3. It's difficult to predict how this will affect the real-time cost, but if simultaneous turn (without neutral battles) is implemented, theoretically, the first week will be played twice as fast, and from the moment when simultaneous turn ends and real-time battles with neutrals begin, the battles will likely take a little longer, but their number will decrease.
I don't know the mechanics of the timer in battle; if it ticks separately for each side, you can encourage it by limiting the time for the player controlling the neutrals and making them do it as quickly as possible. In Heroes 5, there are 4 battle modes in this regard.
- normal (think as long as you want)
- dynamic (slow) approximately 15-20 seconds are given for each of your and the enemy's stacks to perform an action; otherwise, the stack is automatically skipped, the same applies to heroes, but the limit is slightly higher, about 20-30 seconds.
- dynamic (medium) the same as "dynamic (slow)," but the limit is smaller... about 10 seconds for monsters and 15-20 for a hero.
- dynamic (fast) 5 seconds for a monster and 10-15 for a hero.
I don't remember the exact numbers, and the system itself is flexible; that is, I noticed that a certain percentage of unused time is carried over as a bonus to the next unit. If you move quickly at the beginning, you can then take a little longer to think.

4. Imbalance may increase due to the setup - archers and fast melee units will become very dangerous.

Well, besides simple gnomes, golems, and zombies, there's not much better protection than that - and all the other stuff will just be less harmless, which is fair and, in my opinion, even improves the balance, because it's not always possible to split up units in all situations, and not all monsters can be split up, but there won't be any splits at all. And in general, neutrals will take revenge for all these years... now their favorite activity will not be distracting with single units or unnecessary meat, but sabotage and terrorism.

P.S. In my opinion, if the goal is to improve gameplay & balance, things like this should be a priority.
And simultaneous turn and timers are more about convenience. But ideally, you want both.