You're missing the point entirely. You're just banging your head against "Different people learn in different ways". I am saying, that the thing this course, (that I took by the way), is trying to teach students is the skill of writing proofs effectively.
A solutions guide, as you imagine it, would not teach students to write proofs effectively. Since many of the problems in this book are of a research level, many are highly advanced. Many require many multiple pages of exposition to describe the solution effectively.
You would thus have to make a tradeoff. Remove the harder questions and write simpler explanations, so you can write a cost-effective and printable solutions guide. But then the "solutions" aren't actually solutions at all, but vague allusions towards the correct process. The student assumes that the "answer" are these vague allusions, "since that's what the solutions guide says" and the entire point of the class is bypassed in favor of passing more students.
It has absolutely nothing to do with gatekeeping, or cheaters. And quite frankly, I don't believe that advanced mathematics will ever able to be the most accessible thing in the world. And that's just its nature.
EDIT: Seriously if this was Calc, I'd totally agree with you 110%. A lot of people can only learn that stuff by staring at the answer being worked out. But that's not math man, and it's not what we want to teach people in this course.