Heroes 5.5 WarGame Edition - Tactical Edition.

What does rushing have to do with this? A rush is an early attack when the opponent hasn't had time to develop; if development to top-tier technologies happens in the first week, then arriving in the second is technically no longer a rush.

The focus is on dynamics, because that's the most exciting part. You start a match and know you'll finish it today. You play against a live opponent instead of spending many hours fighting neutrals, where it's the same thing over and over again. Long games are tedious, especially when they are one-sided, like clearing neutrals. Sure, you'll play one map like that, then another, but then what? Repeat the same thing constantly? A live opponent won't let that happen if interaction occurs as early as possible.

No one seems to know how to play for pleasure (and I'm not talking about a maniacal obsession with full clearing of an unbelievable map size). One must finish a map in half an hour, because a person's time is limited....

Let's not exaggerate; half an hour is only the time for a single final battle.
Even with fast dynamics, if we manage to compress a game into 2-3 hours instead of 10-30, that would already be an incredible success.
Protracted games are the number one scourge of the entire turn-based strategy genre, especially in the era of active streaming. I've been playing turn-based strategies since early childhood, but I still haven't been able to force myself to watch even one (Karl!) such game on a stream for even 6-10 hours.

If the focus were on single-player, that would be a different story—why not drag things out in single-player? But here it is clearly established: everything is for Multiplayer. Single-player may be supported, but on a residual basis and only if it doesn't harm Multiplayer, the primary mode.

For example, one of the difficulties (specifically for single-player) could feature a doubling of neutrals every week, say (numbers are hypothetical). Then for lovers of long games, there will always be strong, even impossible guards; by the second month, there'd be a hundred or two dragons :)
Only in the Heroes series is it customary to stamp out and slaughter dragons by the dozens and hundreds; there's no epic feel or respect compared to higher creatures :)

Added after 11 minutes

Build angels in the first week, loot Utopia on the 4th day of the game, reach a good build in two weeks.

You won't be looting Utopia on the 4th here, and if you can, such abuses will be suppressed. Appropriate timing for Utopia is 2-3 weeks. Tier 7 is built quite slowly—only angels and cyclops go up, and even then with difficulty, and only for the second player. The first player can't keep up with that tempo. So usually, the norm for Tier 7 is appearance in the 2nd week, although any race can certainly gain access to them at the start of the 2nd week, even if they aren't built in the first. And even in cases where building Tier 7 in the first week is possible, it's far from always the best strategy, as it has a number of drawbacks (primarily, difficult construction, losing tempo in clearing until Tier 7 appears, lagging behind in all other troops since Tier 7 has many prerequisites). But if the race allows and the player sets such a goal—why not give them that opportunity?

It is quite possible that we will tune the taking of Utopia normally for the 3rd week (endgame), but knowing the ability of some players to take incredible guards, questions arise as to how large the guards should be so that they definitely aren't taken in the second, but are normal in the third? And is such a division possible in principle? The more powerful the guards, the more mindless abuse of AI "bug-features" and more hardcoreness for a narrow circle of players, while fixing such abuses might affect the games of the majority of other players.

There is also another very important detail to consider. Unlike the original Heroes, small guards motivate splitting troops rather than just playing with one "fist." I'll just provide a quote from another forum:

There is no concept of a Main Army (MA) like 100+ liches (any passages are easily cleared, no artificial dragging out of the game).

Hero roles:

1) Powerhouses (equivalent to about 5 dragons and above): capturing key objects, killing enemy combatants
2) Combatants (about 2 dragons): clearing, killing scouts
3) Scouts (about 50% of a dragon, starting army): reconnaissance, opening zones, gathering freebies, transport, sabotage, blocking powerhouses

Scouts require troops to clear passages and counteract enemy scouts. A classic "cockroach" (a scout with 1 peasant) will not be able to perform the primary function of a scout—opening zones—which will seriously limit reconnaissance capabilities.

Instead of 1 Main Hero and a bunch of cockroaches—several powerhouses, several scouts, and many combatants. Economically, the most profitable investment is in combatants (maximum efficient clearing). Playing through 1 Main Hero without combatants loses in economy and territory control and is justified only during a rush.

Difference from the original: starting troops are many times stronger, and guards are weaker; thus, scouts are able to independently clear small guards and passages without purchasing additional troops.

(I'll add, "many times stronger" is relative to benchmark dragons)