In your exploration example involving the medical examination, you are calling for multiple ability checks to see whether a character succeeds at the task of investigating a corpse with variable outcomes.
An oversimplification. There are multiple things that can be examined (as mentioned upthread: time of death, stomach contents, wound sites, etc.) And those things could each provide different, useful bits of information. Each one could yield a distinct clue.
Your position appears to be that allowing multiple checks to generate multiple clues would be a bad thing. Yes? No? Maybe I've misunderstood.
In your exploration example involving the rooftop escape, you are calling for multiple ability checks to see whether a character succeeds at the task of traveling to the Copper District.
More straightforward than above... but this is still an oversimplification.
They can travel to the Copper District any number of ways. Depending on context, each way could be fraught with different potential challenges.
Let's see if I understand you: You're saying that the player's declaration of "I hightail it to the Copper District" should be a single action declaration, resolved with a single check. Yes?
So...
If the player chooses to sneak there unnoticed through back alleys, he rolls a Dexterity check?
If he chooses to navigate the rooftops, he rolls a Dexterity or perhaps a Strength check? Just the one, right? Because rolling two checks for this single action is bad.
If he chooses to make some friends at a bar and carouse down the streets in plain
sight, perhaps he makes a Charisma check?
And if he chooses to confront some guards and fight his way there, then he makes... an attack roll? But just one, right, because we wouldn't want two d20 rolls to resolve a single action ("get to the Copper District.")
Clearly this last one deviates. Is it just because it is combat, and is therefore deserving of more time/rolls/failure points/etc?
In both of these examples, you are deviating from the rules. (Therein lies my objection.)
In what way am I describing deviations from the rules? I don't understand that. Can you clarify a bit more? What rule(s) do you have in mind that are being deviated from?
The rules are really awesome. (Therein lies my position.)
Agreed. I'd certainly call 5e the best edition of D&D ever printed.