Yes, MTSG is very contrived, and in no way resembles physical reality, if you are looking at stacks in regions and distances. Two very poignant examples:
- First Situation: the CS has Lee (Army stack with several divisions) in the middle with a Corps each left and right (Longstreet and Jackson), moving forward line abreast.
The action:
First battle: Longstreet and Jackson both encounter enemy stacks in their target regions, and battle ensues in both. Jackson, being the faster mover, arrives earlier in his target region, and battle starts there first, and Lee MTSG's to Jackson's aid.
Second battle: One or two days later, Longstreet goes into battle, and again Lee MTSG's to the rescue.
Comparing game results with reality: Lee battled twice in one turn, in both regions to his left and right. In reality, this would mean that Lee marched first into Jackson's region and took part in his the battle, and then in the opposite direction, into the neighboring region on the other side of his own region, to take part in Longstreet's battle, all within the span of several days.
- Second Situation (Jackson is in Tennessee between Memphis and Corinth, with orders to cross the Mississippi north of Memphis and attack the enemy there. He's a fast mover, his Corps is in good condition, and the weather is good, so he will arrive just in time to kick some Yankee butt. A Corps from the same CS army is sitting in Corinth defending, trying to buy time and delay the Union's advance. (In a strange set of circumstances, the Union is advancing from the south in this case).
The action:
Jackson is one day away from arriving in the first region outside his starting region, north of Memphis, when battle starts in Corinth, and his Corps is called in to help, which it does. After the battle, Jackson 'continues' with his move.
Comparing game results with reality: Jackson, on his way westward, has just taken part in a battle in the region to the east of his starting region: In reality, that would mean that one day before being outside MTSG range, he counter-marched into the region in the opposite direction of of his march, took part in a battle, and nearly managed to arrive in his target region at the end of two weeks. (Actually, in the game this occurred in, he failed to reach his target region on time, because of the cohesion his Corps lost in the battle, plus IIRC the ground might have been muddy too. If successful, it would have been a brilliant Jackson-maneuver, and saved Memphis.)
In reality, Jackson's Corps would have march westward four days, then counter marched to the east eight days, done battle for a day, then counter marched again 8 days, and continued on for another eleven days to nearly reach their goal. That's 28 days in one turn... 28 Days...
28 Days Later!... Jackson's Corps is comprised of fast Zombies!

MTSG doesn't attempt to represent reality in days-of-movement. Turns are 15 days, and withing 15 days campaigns culminate, major battles, with large movements of troops, are fought and won. In the game, the player can only sit and watch as his plans for maneuver from the start of these 15 days, are carried out. There is no opportunity to react to the opponents movement within these 15 days, where in reality, many decision would be made, changes of orders carried out as the situation develops. In reality, an army maintained its Corps, not within days march of each other, but within an hour or less. But in reality, on realizing the enemy's maneuver, plans were overturned, marching orders changed, and all plans from the previous days forgotten. In the game, this is not possible. If in the game, we didn't have MTSG, Corps would skirt past each other with ease making a defense impossible, and the attacker could concentrate an attack with all an army's corps, onto a single enemy corps, without the defending player having a way to react. This is why we MTSG.
It is not at all unusual for battles to start late in a turn. Enemy stacks do not always start in neighboring regions, and poor weather is a fact of game-life. It may not be the most common of cases, but it is far from rare.