Sure they would. They would understand that there's an off chance of the spell being wasted, but in the vast majority of instances the "initiative results"(which they are not even aware exists), wouldn't stop the spell from being effective.
We see that right here in the real world. If what you say is true, then the police wouldn't train to shoot center of body due to the off chance of someone wearing a bullet proof vest. Except that the do train that way, despite the off chance that their shots will be wasted due to the presence of a vest.
Considering that there's the exact same chance for double effectiveness if you roll well for initiative with a spell, I would absolutely take that as a fighter. If I roll badly, I do no damage. If I roll well, I do double damage. The vast majority of the time I simply do normal damage. Works for me. The damage over time works out to be the same as if you have static initiative.
Ok so we all know that we are looking at things within a context of this game., right? It's in comparison to other options that exist within that context.
Police practice shooting for CoM because that is the best and safest option. It produces the most reliable choice. Their is not a better option. Also, most body armor that renders a bullet ineffective instead of simply non-lethal is highly visible before the policeman decides to shoot. So if he sees the heavy gear that can have plate insert he can make an informed decision - perhaps opting for gas if that's an option or containment or waiting for heavier firepower. Key is the body armors that can reduce the effectiveness to zero are rare.
In this 5e house ruled example, we have the exact opposite situations.
The "added thing" that renders a subset of the effects sometimes ineffective even when they work is not rare and not visible.
And the key difference is **there are alternatives** and thatsxehere the rub comes in.
You see, while you go off on damage the effects mentioned were mostly not damage, not double damage but control. That control is initially bought at the expense of extra damage.
So let's do an easy example.
Ray of Frost vs Firebolt.
Both require the to-hit for any effect at all.
One does more damage flat out everytime on a hit.
One does less damage and (RAW) reduces the enemies move for what is pretty much guaranteed one turn of their action.
But add in the house rule of re-rolling order and even possibly not knowing your order when you pick attacks and now that control speed reduction shifts from "trade damage for control" to "trade damage for a random chance at conttol."
That takes Ray of Frost from an arguably balanced trade-off to really not even close. In the context of the game those choices are now not a balanced pair of options and essentially it makes no sense now for them to be presented as such.
Now, one can try the "overall it balances out" but really for most of them that fails to be true.
To give up damage for Ray of Frost, one usually has a specific "need it slower now" need, and the fails vs goes twice does not "even out". This is particularly true in 5e given that more than a few combats dont see lasting that long on many foes.
A good example was a fight tonight vs skellies, where Ray's of Ftost could keep allies from reaching attack range, adding a bit of damage and then the shellie did not survive for the theoretical second move at slow. Here the initiative rework would result in sometimes wasted, sometimes did not matter but firebolts eould still be the 100% alternative.
Similarly booming blade for instance, it goes off once... so the random initiative shaft-me roll gives you the option for it going down before the enemy gets to move or no other gain from the field lasting longer until they move.
So, no, those results are nonsensical in the context of the options presented and they add not a degree of uncertainty or s sense of risky double or nothing but just a sense of "this gameplay seems not very thought out" --- which makes sense when one sees the proponent asking essentially if there are spells that would be hit this way.
There are already built into the options and effects presented chances of success and failure to reach a desired degree of "trade offs" between comparable alternatives. This change, made without due diligence, kicks that for a number of effects and options with the hope that it works out somehow.
Not a gameplay I would inflict on my players, but hey, to each their own.