Pre-qualify the work you have to do.
Whatever system you go with, pre-vacuum is very important, (imho).
If the carpet is loaded with soil, then I would HWE.
Over 90% of the time I encap carpets using a Cimex and a QUALITY ENCAPSULATION CLEANER that will fully crystallize when drying.
A Cimex is not a rotary.
On some others that I feel need that bit extra, I will follow up with a bonnet clean for that WOW factor.
The cleaning solution is most important in VLM methods, a true encap; product will crystallize to a fine powder that will not adhere to the carpet fibres and will be easily removed when the dry carpet is vacuumed.
If you use a mediocre product that does not fully crystallize, then this may well allow the slurry, (dirty moisture), to stick to the fibres and will not release when vacuumed, giving that still dirty look.
In my opinion, encap; products do give superior visual results on synthetic carpets.
With really filthy carpet, after pre-spray agitate with a rotary, (I use my Cimex), then HWE.
Use the "cleaning pie" to your advantage.
Even on some filthy carpets both natural and synthetic, after HWE I have gone over again with a bonnet, removed more soil, and got a far better visual result.
Some carpets just need that "two system" clean.
Sorry for the long post.
Shorty down under.