Your gut is correct. You are entitled to have ALL your parent concerns put in the IEP document. But don't wait until the meeting to voice them. Put your parent concerns in a letter/email to the IEP team before the meeting. This accomplished two things: 1) the team can (hopefully) prepare ahead of time for your concerns and 2) they have an easy way to include your parent concerns in the IEP document - by just cutting and pasting.
Even with this convenience, school districts still seem to push back on putting parent concerns letters/emails in the IEP document, and unfortunately, the federal law regarding the IEP process (Individuals with Disabilities Education Act, or IDEA) does not specifically address parent concern letters. However, it repeatedly mentions "parent participation" as a high priority during the process, so I would argue they are not allowing your full participation if they don't put in all your parent concerns - whether you state them verbally at the meeting or via a letter/email.
Although the IDEA does not specifically mention parent concerns letters, Lisa found a VERY helpful sentence in the comments to the law's passage (which basically sets forth in detail what the law means), as follows: "Parents are free to provide input into the child's IEP through a written report if they so choose." See the link for Lisa's entire blog on this issue below. This is something you can point to if they refuse to include your parent concerns letter in the IEP document.
As far as why a school district does what it does, your guess is probably as good as mine. Their excuse that the concern has to happen "frequently" is not a valid one or more importantly, one that is required by law. Some school districts try to avoid documentation whenever they can. But I wouldn't worry about the "why." Just know what YOUR rights are and if they provide a reason denying your request, make them show you the reason in a written law/statute, state guidelines, or school district policy. If they can't, go with your gut and tell them you want it in the IEP.
https://adayinourshoes.com/parent-concerns-on-the-iep-parent-letter-of-attachment/#h-where-is-the-parent-concerns-letter-mentioned-in-idea