There are two ways to interpret that sentence, and it hinges on a weirdness of how English uses the indefinite article.
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
The usual interpretation of "a threat" here is that it means "one threat". If that is the correct reading, your question is the result. Is it correct though? This meaning would require that surprise is a relationship between two individuals, so that the dire wolf could be surprised by the rogue but also not surprised by the enchanter.
Is this how surprise works? It turns out, no:
If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends. (PBRv0.2, p. 69)
Surprise is not a relationship between two entities, it is a state of a single entity. It's impossible to be surprised by one opponent but not surprised by another.
Is there another way to read that sentence about "a threat" that makes surprise sensible as a state? As it turns out, yes.
"English is funny that way"
Another use for the indefinite article, which looks identical to the "one threat" meaning, makes the sentence in question
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
mean any threat at all, not just one. If this meaning of "a threat" is how it's being used, then that means only creatures who notice no threat are surprised.
Because this reading is perfectly normal English, but ambiguous, we need to confirm the reason by looking for clues in the surrounding text. That confirmation is in the definition of surprise we looked at above: being surprised means being completely surprised, which only makes sense if it happens when no threat is noticed.
So the dire wolf is not surprised, because it did notice a threat, as opposed to not noticing a threat. (See how that makes sense put that way?)
On the plus side, the champion and the rogue don't need surprise to have advantage on the dire wolf, because that doesn't rely on surprise, but rather on being unseen, and being unseen is a directional relationship, not a state.
I have experience playing the low levels. I can briefly summarise the impact as follows:
- It will make encounters much harder. With many characters dying in combat, and possibly a few total party kills as well.
- This can be demoralising, but some players might be up for it.
- But something perhaps easily overlooked is that it removes a wonderful suspense building mechanic from gameplay. With current rules, a character going down leads to a change in tactics to keep the party member alive. By removing death saves, this falls away. And the only decision is: Is it time to flee, or can we still win this?
Characters in our party are regularly taken down (which would mean death with the house rule) and require in-combat healing to bring them back into the fight. Failure to do so in some cases would probably have resulted in total party kills.
In your comment on Dale's answer you consider:
players were encouraged to retreat if the going got tough
The problem with this is that there's not necessarily enough time to make an escape. The fact is that even as it stands (without the house rule): "level appropriate" monsters have a decent chance of 1-shot killing most level 1 characters. (When I say decent chance, I'm not even talking about needing a critical hit.)
NOTE That a single CR 1 monster is considered level-appropriate for 4 level 1 characters.
Consider a Specter (CR 1): It does 3d6
damage with +4 to hit. This is only an average of 10.5 damage. But it's special ability states that if a CON saving throw is failed, the target's maximum hit-points are reduced by the same amount (and if reduced to zero, the character is dead).
Of course if you and your players are up for a much more difficult challenge, then then feel free to tweak accordingly.
However, changing the death-saves rule is not the only way to do so. Remember that removing death-saves also removes a tension creation mechanism of combat. So instead of removing death saves, consider the following ideas:
- Have your monsters fight more "intelligently". Let them make good tactical decisions, and you'll see difficulty ramp up without any extra work.
- Tweak difficulty of encounters by adding monsters, or using stronger monsters. This might require a little more planning on your part, because it can be a little to easy to overdo it.
- Reduce the character's opportunities for rest a little. This means they rarely recover their abilities between encounters. It has a similar effect to the second point but is possibly a little easier to manage.
Best Answer
This is going to be a poor idea
As other answers point out, this is going to make save-targetting spells significantly weaker, but there's also another problem you might not have thought about.
Being at 1 HP is more dangerous than being downed against big threats
This is going to leave a lot of players in combat running around with exactly 1 HP, which is prime instant-death territory. Most monsters are perfectly okay with letting a character make death saving throws to stabilize themselves, but they're not quite so okay with being stabbed in the back. (citation needed). Simply put, while downed, you are not a threat. When you're still standing at 1 HP, you're a threat and need to be taken out.
Example:
Bob the Dragon does his breath attack on Billy. Billy has a max HP of 35. The dragon deals 60 damage, but Billy succeeded on his save, so he only takes 30. That's still enough to down Billy who already took a beating from a Goblin earlier, but instead of going down, he's now at 1 HP.
That won't do, so the next turn Bob swipes at him and gets a crit. He deals 38 damage in one hit, enough to instantly kill Billy.
This will be even more obvious at lower levels, where succeeding your save against a spell might leave you standing at 1 HP next to an ogre who can one-shot kill you now even without a crit.