Airway width/wx deviation

[Slo Moe]

Absolutely ALL deviations need an approval from the ATC.

Only an emergency or a TCAS RA would allow something else.

Example: There might be another aircraft on an opposite track
6NM offset of the airway centreline and if you deviate 2NM just
on the right spot you would be almost head on for a moment.
You might not even hear the other traffic on frequency, it might
be coordinated over the phone, or via the radar screens
(silent coordination).

At least the ATCO wants to keep his/her separation, if the minimum is 5NM
at that airspace. As a pilot you most likely will not know which is the
separation minima in different parts of airspaces. They vary
a lot depending on many factors.RNP does NOT tell the separation minima.

Do you want to try to guess which
separation minimum the ATC is using this time?

3NM
or
5NM
or
8NM
or
10NM
or
17NM
or
20 NM
or
2 minutes
or
3 minutes
or
10 minutes
or
80 NM

or something else, just to name a few.
I would rather stick to the clearance.