This doesn't address your question as to why it is needed/what it is for, but I think I know why it wouldn't go through, even if you have the correct name control.

It seems that every year there is at least one trust/estate which needs an EIN and which I find out about right before the filing deadline.  Despite having the CP575 in hand, the IRS computer system takes an extended period to recognize that the EIN/name control is valid.  So if you get the EIN on Monday and attempt to file something that week, it is rejected.  In these instances I always end up paper filing, whether the actual return or more likely, the extension.

Now when I go to file the actual return several months later at the end of the extension period, it flies right through.  I am wondering if that was your problem here.  You had/guessed the right name control but had so recently gotten the EIN that one part of the IRS hadn't caught up with another part of the IRS and that caused your rejection.