This started out sensible; you can't get insurance coverage to go solo in that helicopter or twin so your CFI rides along to make this operation legal. Hypothetically, there is no assistance rendered and the "PIC" is entirely the "solo student" (no helping or hinting). Then this morphed into single engine aircraft like a Piper Arrow and as examiners we start to wonder what level of solo compentence is actually present. Hypothetically a pilot can get to be a flight instructor and have only been "actually solo" (alone) in an airplane for five hours! Has this potential commercial pilot ever been alone in an aircraft, possibly scared and entirely on their own? Without this level of courage and self-efficacy there is something missing in our future pilot. Here is an FAA interpretation from a helicopter school and some other reference material. John Lynch added some context back in the day (no longer regulatory but valuable for FAA original intention). The key for examiners is to make sure the time was correctly logged as 61.129 time (assisted PIC), and then it can count in a under "solo time" and "total time" for a checkride. A recent FAA Letter of Interpretation here. Interestingly, it seems the government also wants the 61.129 time not to be mixed between solo of "supervised PIC." This is from the Grannis letter: "The language of the requirement in §61.129(a)(4) is clear that a pilot must choose either to log the 10 hours as solo flight time or log the 10 hours as flight time performing the duties of pilot in command with an authorized instructor on board. " One result of this new interpretation is that a new CFI could potentially (legally) be certificated with only five hours of solo time in an aircraft...weird FAA trivia (and pointing out that legal does not necessarily equal safe or smart)
This is one of the most often misunderstood and abused rules in aviation. Flying clubs are often guilty of "arranging CFIs" or indicating a preference which the FAA clearly indicates is not in the spirit of the rule. The "Lowenstein Letter" helps to make 14 CFR § 91.409(b) clear. Additionally, this AOPA position piece clearly reiterates what the FAA is stating in the letter; if the renter freely chooses the CFI with no influence or preference from the owner/operator (just like an A/C owner) then there is no legal need for a 100-hour inspection.