Becoming a carpet inspector will make you a better carpet cleaner. One reason is it will force you to learn a great deal more about carpet than you would otherwise learn, but even more it will change how you look at carpet problems.
We as cleaners tend to always see issues as cleaning related (especially if other people are cleaning it), and assume when we see a problem that its bad technique, bad cleaning agents, bad equipment, etc.
I will never forget being called to inspect a carpet in a major university. The traffic areas had a strong green "discoloration" that looked like a cleaning agent residue gone bad. From a carpet cleaner's perspective I would have been doing pH tests, looking for indicator dye issues, etc.
It turned out that this multicolored carpet had three colors present: Gold, mauve, and green. When I used a pocket microscope I could clearly see that the gold and mauve fibers were deteriorating and looked like broken glass. Since only the green ones remained intact, it created the "green discoloration".
Had I not approached it as an inspector, I don't think I would ever have thought to look for that issue.
In that way, inspector training would help you.
Again, just don't see it as a springboard to "making friends and influencing people" you want as customers. You'll be seen more like a "workman's comp doctor" in more than a few cases.
It is a nice side income when pushing a wand is no longer a desirable option of course.