I’ve done Remembering the Kanji, all the way through, plus the extra thousand kanji in RTK3. It has its strengths and weaknesses compared to WaniKani, which is what ultimately led me here, so I could learn both.
Describing it as “connecting random words to random shapes” misses the point. It’s more of taking a few months out of one’s Japanese journey to get familiar with the kanji, learn to tell them apart, and making each one a unique concept in your brain with its own file that you can start tagging with other information about that kanji.
It’s a bit like how little kids study the alphabet before phonics and reading. It’s hard to think of a word as “circular shape with a gap on the right plus triangular shape plus shape with a right angle” but once your brain sees that as “C - A - T”, it’s a lot easier to learn what it spells. Likewise, looking at a word and having it register as “study - exam” puts you in a lot stronger position to learn “school” than the 18 strokes of jibberish it looked like before studying any kanji.
Put another way, you know that tab in WaniKani’s vocabulary lessons where it says this words is made up of such-and-such kanji and shows their names and asks if you can guess what they might mean together? Well, after finishing Heisig, your brain will show you that tab for any Japanese word you look at. It’s pretty cool!
Of course, what it doesn’t show you is the tabs with the reading and meaning, which is what ultimately led me to try WaniKani. Heisig takes a stab at teaching readings in RTK2, but it’s pretty hit or miss. There are some good insights (especially what he calls “signal primitives”) but for me they work better as hints to help learn other methods than something to be systematically studied in their own right.
WaniKani does a much better job of building kanji to readings to vocabulary. Heisig gives you the radicals to kanji part and then kind of turns you loose to use that how you will. Heisig, on the other hand, covers stroke order and writing of kanji, which WaniKani ignores (less important now that so much is on computers, but still part of a well-rounded kanji education).
In and of itself, WaniKani is also better at providing mnemonics. Heisig starts off providing detailed ones, then gradually starts leaving coming up with them more and more to the learner. But… there is an amazing community over at Reviewing the Kanji who have a page for every kanji with dozens of user-submitted mnemonic stories for each. If there is anything equivalent for the WaniKani method, someone please point me to it! The Crabigator’s kanji stories are usually pretty good, but when they don’t work for me, I don’t have a good source for alternatives. For radical-kanji I can always fall back to how I learned it from RTK, but for kanji-reading mnemonics, I could use more resources.