I play Old School and in casual games we have a house rule that we draw two each turn, with no discarding required in the first turn only. It has several advantages:

• dramatically reduces the likelihood of mana flood/screw.
• it speeds up games, since you generally play a land and cast at least one spell per turn. Otherwise, with typical draw one, players tend to empty their hands quickly and the game slows down dramatically.
• it decreases the effectiveness of control decks like The Deck, which aren't fun to play against anyway. It increases the effectiveness of Aggro styles, which are more fun. Creatures are really janky in Old School and they need as much help as they can get.
• it reduces the advantage of Library of Alexandria, Braingeyser, and Jayemdae Tome, and reduces the disadvantage of Mind Twist, any of which can be nearly fatal in Old School matches.

There is even an Old School variant called "Gentleman's Rules" that bans Library and Mind Twist because they are so powerful in single-draw. In double draw, they are not a problem.

The only downsides:

• cards that punish card draw get much stronger. Chains of Mephistopheles and Underworld Dreams become very strong, almost problematic. If enacted in a tournament, it would definitely change the meta (maybe that's good!). We would likely have to restrict these.
• Sylvan Library becomes very strong, and may need to be restricted.

Some of those factors may be relevant to Commander. Definitely try it out!