Getting back to the original question, no, don’t buy your own aircraft and expect it to be viewed as the equivalent of having a JOB in aviation.
You actually want to have 1500 hours experience for your ATP, not three hours of experience repeated 500 times. The statement about
As a flight instructor, you'll undergo several more evaluations to get the ratings, then by a school to hire you, then training and evaluations during your time with the school, and your students will be examined, and their success will reflect on you. This paints a clearer picture of your character and ability than simply buying an airplane and flying it around (because you can)
may have been inelegantly worded (or not) but it is in fact true. Any job where your flying is SUPERVISED will be a better resume’ builder than any flying you do in your own aircraft unless that aircraft requires you to have a type rating (which is another way of saying there is a disinterested arbiter attesting to your competence). Don’t take it personally, people have been caught pencil-whipping their logbooks. While you I’m sure would never do that, the fact that others have and have been caught at it makes such self acquired hours a little suspect.
That’s not to say that a CFI position is your only path acceptable to getting those hours, it certainly is not, but the credibility of doing the flying AS EMPLOYMENT rather than flying “random cross countries” is a real issue and you ignore it at your peril.