This is how it works in our school district. Two different examples, because both of my kids had different experiences.
Youngest: Was in Early Intervention. Transitioned to SpEd preschool w/ an IEP, then into elementary with an IEP. Nobody questioned his diagnosis, he was already in the system so the transitions were dealt with smoothly. And as far as I can tell, he got all the "standard" autism stuff, without being put into a track.
Oldest: Parent requested eval in 3rd grade but school staff said they weren't concerned so they didn't pursue it. Parent requested eval in 5th grade. Parent had long annoying meeting with SpEd coordinator, classroom teacher, and principal because child was falling thru the cracks due to the inability of the school to *do something*, please. The school squeaks in evals in the last possible days it can.
The eval for math LD confuses me. The test they ran put DS slightly delayed, but only a couple of months and not enough for LD. I look at the test. It has very basic math, I see nothing beyond multi-digit addition and subtraction. This is not 5th grade work. At the time, they were doing multi-digit multiplication and division and decimals. I question it. I understand, yes, that it is a standardized test used all over the US, I get that and that was certainly pointed out to me, but I don't think it is a very good test. I don't expect our little ole school district to buck the system and say the standardized test used all over the US isn't accurate. However, people please, a child takes a test that has 3rd grade work on it, does pretty well, I don't see how that makes him not LD as a 5th grader. But anyway, nothing can be done about it.
There is discussion about DS's diagnosis (currently ADHD) and that I have no intention of upping his meds due to undesirable side effects. The Aspie screening is borderline, relying heavily on parent input, as the teacher hasn't noticed much. An IEP for OHI is put into place to shut up this particular parent.
After it is in place, the SpEd teacher (the one in the trenches) sees that DS has a great deal of trouble in math. She takes it upon herself to go beyond the IEP and tutor DS three mornings a week, before school, which the parent is more than happy to take him to because it confirms that she's not an idiot.
The teacher expects DS to remind her about his accomodations. DS can't remember to brush his teeth in the mornings

much less remember to tell the teacher he gets to go to a different room for his test. The teacher routinely sends home graded work where DS is marked down for bad handwriting. (like spelling tests where she thinks they are spelled wrong, but they're not, he has messy writing) DS also has other things to do, for example he is supposed to go to the nurse after lunch to brush his teeth (long story) but they put it on him to remember, even though they know he doesn't remember stuff. I guess I'm supposed to call the school daily to remind them to remind him? The parent
gives up and prays the next year will be better.
The "rumor" is that once the child gets older, like in the next year or so, the middle school and junior high like to try to drop IEP's if they're fairly mild ones. You know. If the child only has minor modifications, they try to figure out a way to dump the IEP. I spent way too long trying to get one in place.
While it seems like everyone else has a lovely system in place that works the way it's supposed to, that isn't the case for every school district. Ours follows the law. They know the law. However, I personally see a difference between the letter of the law and the spirit of the law. Maybe because I'm on the other side of the desk.