I have played a few sessions of Labyrinth Lord. I rolled up a character who had completely average ability scores across the board. The only things that distinguished my character from any other fighter would be his equipment and my 30+ years of gaming experience, approaching each battle with caution and fear. I think I rolled 2 HP at first level, had 0 bonus to hit or to damage.
That character was attacked in an ambush from a terrible wildman. There was no degree of skill or good playing I could have done to succeed in the adventure. I couldn't reason with him, I couldn't avoid the attack, and the only thing I could've done was to not go on the adventure.
I don't know what luck could have made my character more survivable, but RAW, OSR games are so punishingly lethal that advancing a character is impossible.
Give a character a reasonable chance to survive an initial attack, and we're on to something. Make a character better than your average kobold or goblin, and we're talking. I don't need 15+ HP to start with, but maybe 8? But when you're worse off than the average monster you're fighting at 1st level and you're often facing the same number (or more) of them, and that's just not fun.
All this said, I came into the hobby at the start of AD&D 2nd edition, so my base level was not established by 5e. Something in between 5e and OD&D would be my ideal. I just haven't been able to find the system.
A common house rule in Labyrinth Lord / B/X is max hit points at 1st level.
I'm an experienced DM in OSR games... my guess is that the DM just decided to have the wild man attack with surprise. In which case that sucks. But the rules make that situation extremely unlikely.
In B/X (from which Labyrinth Lord is derived) monster reactions rarely result in automatic attacks. Attacks Immediately only happens on a roll of a 2 on 2d6. This is little under 3% chance. Surprise happens only 33% of the time (1 or 2 in d6). So using the rules of the game, a wild man attacking immediately with surprise is 33% of a 3% chance... just dumb luck. Sometimes the bear eats you.
More often than not, reactions result in may attack, indifferent, no attack, or even friendly (the opposite of attack immediately). May attack and indifferent allow for the opportunity for the players to use their skill and tactics to either avoid combat or improve their chances. No attack means the monster wanders off.
I think a lot of people who run old school games (or have run them back in the day) ignore the Reactions rules. I think they are VITAL to a fun game experience. Once you use them, you practically stop getting the experiences you describe and you start opening up interesting interactions with monsters.
Personally, I like the punishing lethal aspect. It makes me approach the game, in character. "How do I survive in a deadly environment". I can't rely on my hit points or powers or special abilities to cover up for my mistakes. I have to rely on my own decisions and sometimes I'll screw up and my character will die. My response will be to roll up a new one and learn from the mistake. It's only a game.
That being said, it's not for everyone and it's not something I want all the time. I have recently discovered
Low Fantasy Gaming. I haven't played or ran it yet, but from my reading, so far, it looks to be a good candidate for that in between 5e and OD&D experience.