It's a complement, not a substitute: 

1. I find Anki/spaced repetition extremely useful for mastering the vocabulary of a foreign language (or, in non-language settings, getting the basics down pat)
2. But speaking fluently requires -- un(?)-surprisingly -- actually speaking

But mastering those basics is extremely useful!

As Michael Nielsen puts it: imagine trying to write a French sonnet if you have to look up the translation for every word you think of using. Mastering the rote basics is essential, in many settings, for mastery of the larger project -- and that's what spaced repetition does well.

I wrote a post about this recently. Spaced repetition/flashcards are for building broad knowledge. What you want is competence, which comes from immersion. Both are useful forms of learning, but they are distinct and built differently.

I think your plan of finding ways to incorporate Korean immersion into your life is exactly the right way to go.

A large chunk of learning any language is memorization - a lot of memorization. Children do it unconciously without any effort or special tools, but they still effectively memorize thousands of words to become fluent in their native language. After a certain age, most people's ability to easily learn thousands of words in a new language just by exposure gets heavily nerfed, but if they want to learn a new language, they will need to somehow be able to understand and produce thousands upon thousands of words in the new language. The best tool I know of to accomplish this is SRS. When I was living in Denmark (I was 16 at the time), I learned and maintained a sizeable inventory of words over the course of a year using SRS (I got many compliments about my vocabulary towards the end of that time), and it was a massive boon to being able to use the language effectively. It was not a substitute for actually practicing it (or other methods of practicing other aspects), but a very useful complement to real-life conversation.

I also have found Anki to be useful for learning concepts in mathematics and physics - again, it doesn't serve as the entirety of studying, but a very valuable complement, alongside reading technical expositions of the concepts and solving problems that make use of the concepts that I learn and reinforce using SRS.

Other things I use Anki for include memorizing poetry, remembering different musical riffs and motifs, practicing problems for chess and go, maintaining various English words (such as retrograde and prograde, leeward and windward, "junoesque", remembering when dawn and dusk are [I used to get these mixed up often], or how to spell "hors d'oeuvres"),  various facts (such as that the moon is waxing when I can see it in the evening, and waning when it is visible in the morning, or the composition of the British House of Lords, or the basic idea behind how solar panels work), the flags of different countries, as well as the coordinates of various cities around the world, and various other things that I might forget, but want to remember.

My spouse has been learning Korean for two years on Duolingo, which also uses spaced repetition, with approximately no days missed, and learning has been slow. I think Anki is much worse as a primary language learning tool because it doesn't remix particles to give you new sentences to chew on. 

Where I find it shines for me (I review my cards ~2/week):

• English vocabulary
• Programming language syntax
• Concepts that can be distilled into bite sized info chunks -- it doesn't substitute for understanding, but as a person who's better at memorization than concept-processing I find that memorizing the keywords and relations of a topic primes me to take in more when I read an article about how all the concepts hook up together. This works for database concepts but not quantum mechanics.
• 1~3 sentence text designed to change some thinking pattern (e.g. I have an semi-phobia of insects but have had one really nice experience watching one, so I might have an Anki card prompting me to remember that)
• Strong preferences my friends have ("Julie really hates spoilers")
• Helping install TAPs

This doesn't directly answer your question, but I think it could be extremely helpful nonetheless. You might find it helpful to read up on mnemonics. Mnemonics take advantage of the way our brains naturally remember information best and are pretty east to use. If you want a fun read will whet your appetite to learn memory techniques check out "Moonwalking with Einstein."