I'll use English as an example because I happen to know lots of trivia about it. I think it is similar for other languages. The average educated adult native English speaker knows about 20,000 "word families" of vocabulary. A "word family" is similar to a word, but the word family includes all conjugations of the word and all compound words (so the "police" in "police station" or "police state" is part of the same word family).
The average 3 year old knows about 1500 word families. By age 5 they know about 5000 word families and improve their vocabulary about 1000 word families per year (about 3 per day) until the age of 20. Some people have vocabularies up to around 60,000 word families (for example if they have a very technical job).
When people study in school, they tend to study lists of vocabulary up to 1000-3000 words (not word families). These lists often include ridiculous words like "unemployment". Anyone studying a foreign language should look at their word lists. If you have 5000 words, you should be asking yourself, "Would a 5 year old know and use this word?" And then you should be asking yourself, "If this list has this word and a 5 year old would not use it, what word is not on this list that the average 5 year old would know?" Then you should learn that word :-) (bodily functions are usually included in that list and I have to say it is extremely important if you ever need to go to the doctor!)
There are only about 1500 grammar structures in basic English (although there are lots more set phrases that can be used in grammatical situations) Basic fluency starts with simply being able to use the language in a variety of situations. One of the problems with many language courses is that they start the student memorising grammatical structures (mainly because it is really easy to test and makes it appear as if the student has made progress).
However, I recommend finding a 3 year old to talk to. Take note of the grammar that they can use (it's not much!). Take note of the vocabulary that they can use. When second language learners are at the 1500 word vocabulary level, this is what they should be realistically aiming for. Between the years of 3 and 5, children acquire most of the common conversational grammar. They can do it quite naturally because they can speak easily from about 3 years of age on. Children of that age do not require specialised instruction on language -- their parents are more than sufficient.
Finally, a couple of important notes. It takes children about 12 years before they are able to have adult level conversations. Before that, they are unlikely to understand the news, or even movies that are not aimed at children. Even then, it takes until they are in their teens before they start speaking and listening like an adult. We tend to think of children as having underdeveloped brains, but in reality I think they simply lack the language skills. Children that have exceptional language skills at a young age are often thought to be exceptionally bright and often it is not the case.
Even if you learn as fast as a native child, it will take you 15 years to be able to learn adult level conversation and reading skills. Luckily, second language learners can actually learn a language faster than children, but most learners have completely unrealistic expectations (by an order of magnitude).
Finally, there is a period in language acquisition (known as the "closed period") where you can generally understand what's going on, but you can't speak. Virtually everybody goes through this phase in their first language and most second language speakers also go through this phase. Some polyglots have found mechanisms for bootstrapping through the closed period, but in my experience it takes a considerable experience with language learning to figure out how to do that.
In general, sink or swim works fine if you are past the closed period and is absolutely dreadful if you are not. There is a reason why children are tired and cranky and prone to emotional outbursts. It's incredibly tiring and frustrating not to be able to communicate. (OK, there are other reasons too ;-) ). It is super important to accommodate the closed period (which will be different for each student -- and can last years).
My personal technique is to teach fluency without worrying about specific vocabulary or grammar. I don't use lists, but rather use simple conversations as the guide for what to talk about. I use grammar as a tool to help explain language, not as a subject in itself (although learning grammar taught completely in the target language is a super fun way to learn the language if you happen to enjoy grammar, as I do). My main goal for beginners is to get them past the closed period. After that, you just need to grind (whether that's watching children's TV shows, or reading books, or having conversations with accommodating people). One famous comic/talent in Japan (Pa-kun) came from the US and learned Japanese to practically native level by simply going to the bar every day and talking to the regulars there. It's a great technique IMHO.
Class size can be much larger that 3 because the students can ideally talk to each other. In fact, students should be jabbering away all the time. Teachers need to model the language, but they shouldn't be the ones speaking all the time. For me, an ideal class size is between 8 and 12 (depending on the students). Very small class sizes have he downside that it sometimes puts unreasonable pressure on individuals, which lengthens their closed period. I have specialised techniques to deal with up to about 20. Past that, I never found a mechanism that works (but I only did it for 5 years, so there may be someone who knows of a way that works).