A brief note on how we used thieves in OD&D/AD&D (1e) successfully.
I understand what I'm about to outline may not jell with everyone's favorite play-style, and that's fine. With my original OD&D group (79-89) in which I was a player and with my (now adult) children as the DM (2012-2022), this is how we did it.
To put it in context, can you imagine a D&D variant in which every PC was a ordinary human, with d6 HD and an average chance to hit? No classes at all, no special abilities? Just roles to play in a party. It would be like the modern military.
Some would invest in armor and weapons, other would handle the heavy ordinance, and some would be lightly and mobile in order to scout the territory and report back. You'd also need a medic of course. These are your fighter, magic-users, thieves and clerics.
They are roles
in a party that need to be played...again not really "classes".
In the non-combat stages, the scout/thieves are critical. The are willing to take the risk of moving out ALONE in front of the party, stealthily because they aren't in armor. Discover what's ahead and "report back" (which often doesn't happen for various reasons). Even if they are not powerhouses in combat, they get to do the lion's share of exploration in solo mode. Often the other party members are far away...and the other players listening (and making suggestions---we didn't care if that's "meta", they hear stuff, they say stuff---it's part of the fun).
It's a dangerous job, but it's also a fun one. Player who enjoy playing thieves tend to be natural puzzle solver, explorers, and strategists. They also get to be unabashedly neutral and driven by self-interest. That doesn't mean back-stabbing or betraying the party...but it can mean quickly pocketing treasure they stumble across before the party arrives. They also tend to get all the stealth-magic items.
OK. So their move-silent and hide-in-shadows percentages are bad at low-levels. Well, everyone
is bad at the low levels! Take the poor magic user with 2hp and a single sleep
spell---it can be a very passive role they play when things heat up. And I think that's the crux of the Thief-Haters' problem---these are sophisticated, adult players, intimately familiar with the rules and know their chances to a tee. You can pretend otherwise, but these are really the character build min/max'ers in disguise.
Folks need to chill a bit and stop trying to optimize. It's ok to suck, a little. Take a page out of @Malrex
's book and play a librarian.
The important things about the classic play-style (as I came to know it, and saw it work in two decade-long stretches that did not exhaust the player's interest) is that those class-mechanics are secondary to the general "I am a [human] being in this fantasy world, interacting with things". Combat happens, but (good) players generally try to avoid it unless it's a cake-walk.
In a non-combat heavy, interactive world in which class is not of ultimate importance...thieves are essential.
Someone has to play that silent scout role for the party. Remember, in true OSR/classic-play there is no assurance of balanced encounters, you absolutely need to understand your enemies and avoid things out of your league.
Perhaps the thief-class's function was almost broken by WotC with their late-edition, player-catering rule mods. Since I've never played any other way, I never thought for a moment the class was broken (in OD&D/1e).
1) The most successful thieves have always been hobbits.
2) We also always let them use short bows.
Lastly, as EOTB reminds us, the thief abilities are to be preternaturally
quiet or hidden. It goes above and beyond what a normal person could do, which goes hand-in-hand with the notion (for me) that very seldom is a roll required when a thief is acting as a scout. I would, for example, rule that a a hyper-alert thief sneaking ahead in a dungeon has almost no chance of being surprised.
All that said, the-party-rushing-in-to-rescue-the-theif is a common motif. As DM, I hand-waive away knowing he's in trouble, despite the meta-communication implication, but will leave other obstacles (like traps, secret-door detection, path bifurcations, etc.) in place.
Hope that explains my stance on (and love for) AD&D [1e] thieves.