I’m sorry you’re having trouble.

You can always touch & hold a message, & select “Copy” to export an individual message. You can also screen shot your messages, or simply view them in the app.

How does not allowing batch export of sms messages to other apps stop you from accessing them?

That's useful if you want to share a couple of messages with someone else, not if you're looking to archive them. Try finding a message you sent on August 15, 2015, or saving a copy of your messages from 2018–you can't. Again, your tone and choice to pick a strange meaning of the word "access" when it is fairly obvious which definition I am talking about (to the point where you clearly knew what I was saying, since you quoted it) is not welcome.

Saying that one cannot access one’s texts on an iPhone is quite the hyperbole. It would be a bit of a hassle, sure, to locate a text on a specific day if one had many messages in the thread since then. One may have to scroll for quite sometime. I wouldn’t call that blocking access. One can always search for the text based on its content. If one transfers one’s data to one’s new phone, all the texts would transfer as well. So they aren’t deleted by any means, unless one deletes them oneself or gets rid of one’s old device without transferring them.

Batch exporting text messages is an wholly different thing from simply accessing them. The only confusion about the meaning of the word “access” seems to be on your end. You appear to intend it to mean something like “having all the features that I personally want in order to best facilitate the activities I desire to do with the highest priority, disregarding the popular use cases entirely” which frankly is an insane definition of the word “access”, and deserves probably a much harsher tone than it’s been given thus far. The fact that you still appear to be standing by it as a serious definition is even more shocking.

I am using "access" in the same way you might access funds from your bank, which I hope includes the usecase of "I want to withdraw all my money" rather than "I can only take out the last $1000 I put in". I would actually be much more lenient iMessage organized messages better, as many other chat apps do, but it doesn't–I can't search by date, I can't sort attachments by filesize or even given an attachment jump to where it was sent (a big problem if you get sent videos!), if you scroll too far the app scrolls to a crawl, to say nothing of how little you must value your time to want to do that. I am merely frustrated that an app that provides no way of doing fairly common things also blocks people from doing this in any other way, and in doing so effectively does prevent people from accessing their data.