In my opinion, it is less dependent on the subfield than the textbook you use for that subfield. Unfortunately, math textbook recommendations are relatively subjective, with many popular choices unsuitable for self-study, or even study.
With regards to topology, your experience rings true. In short, anyone with knowledge of calculus / basic real analysis wanting to learn topology should read "Real Analysis" by Carothers.
Usually topology is taught after real analysis, extending many results that hold on the reals as the main motivation. But this process is quite abrupt without the intermediate context of metric space, leaving many people confused. It doesn't help that Baby Rudin is quite terrible at teaching these concepts for you. On the other hand, Carothers' book is a paragon of mathematical exposition. It excels at telling you why metric space, topological space, and all the definitions are made that way.
With regards to the parent, I have to say "Proof is left as exercise" is probably the number one thing that forces students to actually read the texts. The best way to learn is to ask ChatGPT after you're stuck, not before.
With regards to topology, your experience rings true. In short, anyone with knowledge of calculus / basic real analysis wanting to learn topology should read "Real Analysis" by Carothers.
Usually topology is taught after real analysis, extending many results that hold on the reals as the main motivation. But this process is quite abrupt without the intermediate context of metric space, leaving many people confused. It doesn't help that Baby Rudin is quite terrible at teaching these concepts for you. On the other hand, Carothers' book is a paragon of mathematical exposition. It excels at telling you why metric space, topological space, and all the definitions are made that way.
With regards to the parent, I have to say "Proof is left as exercise" is probably the number one thing that forces students to actually read the texts. The best way to learn is to ask ChatGPT after you're stuck, not before.