Even still, there remain for me fundamental things about the game (even in cube) that I don't think work well. And no amount of breaking singleton or hand picking card pools is going to get around that. And that's why I'm looking outside the box.
It sounds like different people want different things out of Magic, particularly with regards to variance. We just have to be very careful when we go about reducing variance, not to do more harm than good.
You could make the argument - and many have - that Magic is as good as it is, and riding its current popularity wave,
because it embraces variance. Take a game like chess. It has essentially no variance - I say essentially, because there's still the 'coin flip' problem. Chess is regarded to be a great game, but it's not gaining popularity in leaps and bounds. Then, take a game like war, the card game. It's basically
only variance, and while it may be fun for a while when you're seven, we can agree it's not a well-designed game. If chess is a 1 on the variance scale, and war is 100, then Magic is probably around a 30. There's a significant amount of luck to be had, and it's rare for someone to have a win rate of over 65%, unlike in chess, where you're almost guaranteed to beat someone of a lower skill level. At the same time, the top Magic players tend to keep doing well, year after year, despite all of the luck involved. Poker is a similar animal, and I'd peg its variance to be roughly around 30 on the scale (poker pros on the site, feel free to correct me - this is my uneducated stab in the dark).
Which games are people clamouring to see more of, and organizing tournaments at their homes for friends to come over and play on Friday evenings? It's not chess; it's not war. It's Magic, and it's poker.
These games are popular precisely
because the new player, or the lapsed player, or the unskilled player, can win on any given day against Jon Finkel or LSV. Sure, it'll probably be because the top rated player in the world couldn't draw a second Island to save their life. But having that hope that anything can and will happen is a huge draw to these games, and that factor isn't something that should be underestimated.
From hearing your grievances about Magic, it sounds like you want to make a modification that would take an axe to the current level of variance. Your draw step change change might bring the variance from a 30 on the scale down to a 20, or perhaps even lower. That is not a small change. While your tweak certainly favours the better player - and no one will argue you on that point - you may want to stop and ask yourself if that is what you and your playgroup actually want. Is it something more akin to chess you would rather play, than Magic?
This is why I suggested earlier that if you insist on looking outside of the box, you would do well to consider
other boxes altogether. At some point, the changes you make to Magic will transform it enough that it no longer resembles Magic, warts with variance and all. More likely than not, the folks you've invited over to conceivably play Magic will be less than pleased. And it will be because you pulled a bait & switch on them - you set the table for a formal, sit-down dinner, and told everyone to dress appropriately, but as your guests arrive, you announce that there won't be any food forthcoming, and instead to prepare for a water balloon fight.
If a lower variance game is what you want, I would go and seek out a lower variance game, where its game designers have fashioned all of its cards or game pieces for that exact variance level, and put every deck or archetype through its paces. Not only will that be a more optimal gameplay experience than trying to shoehorn in cards from one game into another - which is what your Magic variant would essentially boil down to - you will probably find yourself facing less resistance from your own playgroup, as you will be announcing loud and clear to the world that, in fact, this afternoon there will be a water balloon fight.