I would guess, if you had a learning difficulty or disability that profound, you would almost certainly be known to SS. They would help in these circumstances.
I can't imagine the application process being that difficult for the average person. The thing is, you can choose a school that is outstanding, with a good reputation and it can be crap. As with one local school, once they achieved outstanding, OFSTED visits were very brief. After a few parents complaining, the school got reinspected, it went from outstanding to special measures.
It would be hard really to claim filling the form was too taxing, when most adults with school age children, easily use social media. You can add onto the comments if that's still a thing, why such a school is first choice. I don't think the allocation take much notice of comments, as for a good school they must get a variety of justifications, why Said child NEEDS to go there.
If choosing a faith school, you have to provide a baptismal certificate. If there's a genuine reason for a certain school, support should be on hand in one form or another.