The main advantage is that by learning higher frequency words, you get a greater "bang for your buck" - that is, if you know the most frequent words of the language, you'll be able to understand more of the words you encounter, and therefore you gain the greatest benefit by studying those frequent words first.
According to Nation & Waring (1997), text coverage in the Brown corpus is as follows:
- Most frequent 1000 words: 72.0%
- Most frequent 2000 words: 79.7%
- Most frequent 3000 words: 84.0%
- Most frequent 4000 words: 86.8%.
So by learning the top 1000 words, you'll know 72% of the words in the average text you read. But after that, there are diminishing returns: the next 1000 words gives you another 7.7% of a typical text, and the next 1000 words allows you to understand just 4.3% more. After that, the returns on memorizing by frequency decrease even more, so learning from frequency lists becomes less useful.
Note that text coverage (the percentage of words that you know in an average text) is important. We don't need to understand every single word in a text in order to understand the general meaning. Some research has investigated what percentage of words we do need to understand. Laufer and Sim (1985) suggested 65-70% should be understood as an absolute minimum for comprehension, but Laufer (1989) (as described in Hu and Nation (2000)) suggests 95% should be known for solid comprehension. Hu and Nation (2000) suggest that 98% of words should be known for unaided comprehension.
Although learning high-frequency words is a good idea, especially when you first start learning a language, frequency is not the only consideration when choosing words to learn. Barker (2007) suggests that "cost" and "benefit" be the primary considerations when choosing words to learn; benefit is partially defined by frequency, but also on personal needs.
So it's good to learn the "technical" vocabulary of your major or field, and it's also useful to learn words related to your interest. It's also beneficial to learn words with a lower "cost" - words that are familiar, that you've encountered a lot recently, or that just seem easy.
Also, although memorizing words has benefits, it is best to combine this with real exposure to words, so that you learn them naturally in real contexts.