I've always believed that the idea behind the solo requirement is to develop confidence as a pilot. When the flight is all up to you, the idea is that you will rise (pun intended) to the occasion, and realize that you are Pilot in Command, you are the only one in the airplane so it is really obvious that you are final authority and responsibility for the operation and safety of the flight.
From a legal perspective, I think the answer to your question might be found in this response from the FAA.
Because this flight time is a substitute for solo flight time, the
pilot is not receiving instruction and therefore cannot log this time
as dual instruction received. The pilot can log the time to meet the
requirements of § 61. 129(a)(4) and log total flight time. Section
61.51 (e) prescribes the requirements for logging PIC time. The pilot could log PIC time under § 61.51(e)(l)(i) if the pilot has a private
pilot certificate with the appropriate ratings for the aircraft.
Otherwise, the pilot cannot log PIC time. None of the other § 61.51(e)
logging provisions are applicable to your scenario. However, § 61. 129(a)(4) permits crediting of the time toward the 100 hours of PIC time required for
the commercial pilot certificate under § 61.129(a)(2). The logbook entry should accurately
reflect the provision under which the flight time is logged.
So the wording in 61.129 isn't really about being alone in the airplane, it looks like this is actually to clarify that that the commercial pilot student (in this case) needs to actually conduct the flight as PIC (with all the responsibilities therein - see below), and if the CFI goes with the CPL student, the CFI cannot log it as PIC time (as they normally would when acting as a CFI), and the time would not be logged as dual received
for the Commercial Student, but just straight PIC time.
As a reminder PIC is defined in 14 CFR § 1.1:
Pilot in command means the person who:
- Has final authority and responsibility for the operation and
safety of the flight;
- Has been designated as pilot in command
before or during the flight; and
- Holds the appropriate category,
class, and type rating, if appropriate, for the conduct of the
flight.
As a final note, I think it gets confusing because 61.87(a) defines solo flight, but only for subpart 87, which is clearly talking about students who have not obtained their private pilot certificate yet:
The term “solo flight” as used in this subpart means that flight time
during which a student pilot is the sole occupant of the aircraft...
The same definition does not exist in 61.129 (Aeronautical Experience for Commercial Pilot Applicants). Noticeably absent from the regulation, however, is the mention of any passengers, so I think the choices are a) the pilot is the sole occupant of the airplane, or b) the pilot is making the flight with their flight instructor, however, the flight instructor is essentially a passenger (unable to log PIC or dual-given time), and the pilot must log the flight as PIC.
I believe this idea that it must be either solo or with your CFI is further confirmed by this interpretation from 2016:
a pilot must choose to log all ten hours as solo flight
time in a single engine airplane or, in the alternative, log all ten hours performing the duties
of a pilot in command in a single engine airplane with an authorized instructor on board. A
combination of hours is not permissible under the rule.
This means you must plan for the 10 hours in 61.129(4) to either all be solo, or all be with an authorized instructor (who is not acting as PIC).