Well, a group of 4 level 1 players should be able to fight a single CR 1 monster. Let's take a bugbear, he can deal 4-18 damage per damage. 12-18 damage can potentially instant kill a fully healed PC already. And the bugbear doesn't even need a crit for it. On a crit, the instant death is almost guaranteed already.
So yeah the HP do seem a bit low on level 1.
I've seen tons of groups that died already at the first battle in LMoP. And many character that got instantly killed on the first battle "boss battle" in LMoP.
There are at least four good reasons for making 1st level characters less squishy:
1) The example you here cite of the fact that a single bit of bad luck can kill even a well played character at 1st level. As a general rule, I feel the game system is doing its job when deaths when they happen, consistently feel earned, in that the players can see that there are decisions that they could have made that would have avoided the death. Preferably deaths occur when the player can see that a long series of decisions led them to a point that they ran out of options: leaping before they looked, rushing in despite "Look at the bones!", separating the party, and so forth.
But the other three are IMO even more important:
2) Frees up the DM to use more elaborate designs and greater variety when designing adventures for 1st level characters. One of the problems that you face as a DM designing adventures for 1st level characters is it feels wrong to make the characters face anything that does more than about 1d3 or 1d6 damage on an attack. In most editions, I've avoided even using orcs against 1st level characters. With less squishy 1st level characters, you can just choose from a wider variety of monsters.
3) Cures the 15 minute adventuring day. I'm surprised this hasn't gotten more attention yet. The big problem from the perspective of a DM with 1st level characters is that it's too easy to exhaust their resources. They have no spare hit points. They have very few spare spells. It's not merely that you want the characters to be able to survive two orcs or a bugbear at 1st level, but that you want them to be able to push through 4 or 6 encounters and a couple of non-challenge rooms before needing a long rest to recuperate. You want the players to do enough in the adventuring day that they feel, "Yeah, we did a lot today." You want them to have some stamina and be able to endure some time pressure.
4) You don't have to rush past 1st level. To me, this is the most damning about the current design. The designers made 1st level go by so quickly, they surely had to know that at some level 1st level wasn't fun. Instead of fixing that directly, they have tried to work around it by saying, "Well, it may not be very fun or very interesting, but at least it is over quickly." This is not a defense of the existing system, and those that bring up how quickly 1st level goes by are proving the original poster's point IMO.
The game has been moving away from squishy first level characters since 1e. The same people complaining that you shouldn't give 1st level characters nonetheless embraced max hit points at first level, or death at -10, or other rules for slow dying, and everyone able to get full Con bonuses. All of these innovations were meant in part to solve the above problems. All have proved inadequate because at the same time they were adopted they tended to inflate the ability of monsters to dish out damage. Tweaking the existing design is I feel perfectly warranted, though you should take care that when you pull on one thread of a system it tends to be connected to a lot of other things and you may need to do other 'mending'.
