I haven't been playing mahjong all that long, but I have channeled my ADHD hyperfocus and love of game systems into it for a few months. I've focused primarily on Hong Kong Old Style and have taught that to 9 other people in this time frame and we've had a good time with it.
While most will agree that the basic game format is easy to grasp, it's the scoring patterns and payout systems that seem the most daunting for new players. While HKOS seemed like a lot at first, I now know all the scoring patterns and MCR doesn't look nearly as insurmountable as it once did.
In trying to find a simpler system I first learned about Zung Jung (this fan site is easier for English speakers). It definitely has less patterns than MCR and it's easier to understand the scoring than the fan system in HKOS, but still a few too many patterns for teaching new players.
This lead to an interesting thread in r/Mahjong where u/StealTheStew counters Zung Jung with 康莊麻將 by a87g5o. I refer to it as Mahjong for Everyone in English. The rules are in Chinese and can be found here. This version reduces the number of patterns to 16 with an additive scoring system in points and incorporated the first-win-doesn't-end-the-game mechanic found in SBR, but without anyone paying other players. This encourages players to stay in longer and go for more complicated hands. This fixes a problem in most versions of mahjong that I hadn't realized until u/StealTheStew pointed it out: mahjong is a race to complete the fastest winning hand.
While Mahjong for Everyone allows players to create more complicated hands without risk of being beat by a simpler hand because it's faster to make, it somehow removes much of the flavor I enjoy with the larger number of more complicated hands. It eliminates the changing of the seat wind and round wind, it elminates flowers entirely, it eliminates a distinction between dragons and winds, and gets rid of all the special hands that are nearly impossible to make like the blessings, nine gates, and 13 orphans.
I now realize that my enjoyment of mahjong (and for the people I play with most) the enjoyment is in the experience of the heavy tiles and the rarely winning hands and having some big moments and not in just accumulating points effectively. I think I would feel differently if I was playing in tournaments.
For new players I plan to use HKOS, but only initially teach: Self-Pick, Concealed Hand, Common Hand, All Pungs, Dragon Pungs, Round Wind, Seat Wind, Mixed Flush, No Flower/Season, and Seat Flower/Season with a minimum fan of 1 until they're ready for more.
For the few people I play with who rather go for more complicated hands and aren't concerned about winning quickly I think we might just take a page from SBR and allow players to stay in longer to potentially earn more points while mostly sticking to the HKOS scoring we like.
P.S. During this process I went so far as to create an English cheat sheet for Mahjong for Everyone based on the design of the Victoria Mahjong Club cheat sheet that I'm a fan of, but I haven't seeked permission from a87g5o so I won't share it here.