In a previous life, I was a NASA Certified solderer. I worked after the USN in the avionics industry, and we had to adhere to those rules.
Tinning is something I still always do.
"Strain Relief" was taught to us in the courses as a certain amount of solder wicked up under the insulation, and in tests they would cut the insulation off and see if we had done it right.
Once the solder flows up under the insulation, no more issues of breaking at the junction or wire and end-of-insulation.
The end-of-tining is now under the insulation, which keeps it from breaking.
Now, if you just "tin" it, and don't flow the solder under the insulation, yes, you'll break the wire.
Conversely, if you don't tin it, the wire, in normal flexing and vibration, will "steel-wool" out and destroy itself.
The tinning also helps mitigate corrosion issues on exposed wire.
Dave