Which D&D are you talking about?
Early D&D (or OD&D) if you wanted a character to sneak past a guard it was DM's choice. In many games that meant a Dexterity check.
If the character was a thief, they got that dexterity check ON TOP of their other checks.
Just because one wasn't a thief did not mean that they could not actually use their ability scores to try to sneak past, steal, climb up a cliff with a rope, or multiple other items.
It was a later iteration that caused players to think this way (as it did not really notate this in 1e so some really weird people had a rule that a fighter could not walk quietly and could not climb things and other such crazy notions).
This got further reinforced with 2e...
But luckily nothing in the rules PREVENTED ability score checks (and prior to Non-weapon proficiencies ability score checks were actually encouraged, similar to how 5e handles many of it's skill systems, but less structured).
However, 3e I think sort of made this an even worse exaggeration of skills and such and it only started to change with 4e (which handled things similar to 5e but all around with a +5 to skills in general (instead of the +2 to +6 proficiency spread).
Your idea doesn't really hold water with the early thief class and how it was handled...though it probably holds water with LATER AD&D 2e and especially 3e.
As far as making the Thief a marksman...the crazy thing that people expect now is that some untrained lackey is going to have the same ability as a trained warrior. That a soldier is going to be just as proficient at hitting a mark as a guy that spends his days buried in a book, or a burglar who spends his time sneaking around.
Having recently spent time with AD&D 2nd Ed and Labyrinth Lord made me realize just how pointless the thief class was. Any character using their ability score to do anything would be more successful than a low level thief. A wizard with a 7 Str is more likely to climb. A cleric with a 9 Dex is more likely to hide in shadows or move silently.
But if a DM doesn't allow ability scores to be used, the thief has like 15% chance to scout ahead and do his job.
Even though I have fond memories of these games and they have their place in gaming history, they are poorly designed.