GERMAN CASES & GENDERS
Ok, so when I started German. I wasn't really concerned about the difficulty as I am learning it at school (i'm way better than everyone in my class though lol), so I didn't really consider cases or gender while beginning to learn it. Then while learning I thought about giving up German and doing something like Spanish, more speakers and 'easier'. But then I realised, and you should too, cases aren't just there to be the bane of language learning but they free up word order and I love this particularly because say if you accidentally begin the sentence with 'den' it can still make sense! Zum Beispiel: 'Den Hund hab' ich gekauft'. And yeah, genders make the language diverse and different and I always wanted to just become fluent in a language, so I started to learn Esperanto. Sorry to Esperantos but I found it so boring, everything was so regular it didn't feel like a language, I just couldn't learn it. And so I began German again. So my lesson is to NEVER NEVER EVER condider the hardness of a language when picking one to learn. Choose one that interests you even if it has 3 speakers, 90 cases, 200 verb tenses and 62 grammatical genders. If you really like the language you will learn it quicker than say French if you didn't enjoy learning that.
While I agree with you that cases are really cool, I don't study them. I notice the case of a word in a sentence and try to "get a feel of it", but I don't recommend someone spending hours trying to get them down pack. Language is easier to learn when you are not afraid of mistakes/ willing to notice things. :)
Just wanted to comment for a couple of things.
I noticed myself unconsciously nodding when you mentioned getting a feeling for case. It really is such a huge step moving from just intellectually understanding to knowing. I also wanted to mention I wholeheartedly agree with your final sentence; making mistakes and learning from them, as well as being aware and consuming as much of the language as you can moves you forward so much quicker than not!
However, I just wanted to give myself as a counter-example of spending hours studying to understand a topic. I realise here we are talking specifically about cases, and that's something I must admit came more intuitively to me than, say, adjective endings, for example; but I still think it's worth noting that before I got a grammar book, I was often floundering with many of the more testing exercises, where knowledge of one or more aspects of German grammar was necessary, and the grammar book really accelerated me reaching the stage where I could just feel it.
Taking the adjective endings specifically, I really put significant effort into learning the tables for the weak, strong and mixed inflections. At first, this meant that I could apply the correct ending in a few situations (generally those in the nominative case) with little to no effort, and could picture the tables I had practically imprinted onto my eyelids in the harder situations, and over time this process became less and less conscious, to the point where I now have a feeling for the adjective endings.
Neither your method nor mine is going to be the perfect method for any one person, which is why I just wanted to add that whilst for some noticing rather than studying to get a feel may be the way that clicks for them, for others the opposite may be the case.
I don't think studying is bad--and I mostly take my approach due to the lack of time I have per day to study German. Like you said, each method will benefit different people differently. On a side note though, I do look at tables to confirm what I am noticing or to check my work.