Don't heed the undeserved skepticism. You will want to tweak, but it's not a big deal really; in fact it has some nice effects and can become a useful kit in your toolbox if you want to rework the game's damage values.
D4s are now now scrappier but not by enough to make them ever better than a d6. A d4's average damage goes up by about 0.63 damage per roll, while a d6 only goes up by 0.58. That's only a 0.05 damage relative increase, and the gap between then was already 1 full average damage.
However, 2d4 was already better than 1d8; but now it's
quite better at an average of 6.26 damage -- that's close to d12 level of damage. So you will want to reserve multi rolls to things you want to do lots of damage. Spells become even deadlier; as does sneak attack -- these are not inherently bad.
Here, I'll take some of the heat off your post by explaining how I run crits in my game

For every 5 higher an attacker rolls than the target's AC, the attacker gains 1 stack of crit damage in addition to regular damage. Crit damage is the attack's maximum damage by the dice.
So a fighter dual-wielding a longsword who normally does 1d10+3 damage and scores 2 stacks of crit damage would do 1d10+23 damage. Low vs high level matchups are absurdly lethal, and this was my intent.