I haven't actually done a low toughness run, but toughness does seem to act as a general indicator of your character's dominance, and having high toughness unlocks some unique dialogue/scene options for humiliating/degrading the girls as well as acting more dominant and such.
I think some of the questions about inconsistencies in writing are because the players asking did mainly a high toughness playthrough. The toughness score is not only about Edwin´s general resilence, but it is also an "asshole score" indicator.
The low toughness (up to about 12 points IIRC) Edwin (esp.with helper as motivation) is a really nice guy and has the inner monologue and feelings fitting for it. The 12-18 points Edwin is still really nice, but has made some "hard" decisions.
At about 18 points Toughness TD once called the character "mischievious". He still is a nice guy, but can be harder if the situation "demands" it. This Edwin is still nice and looks out for his friends, etc., but can do some actions, if he wants or needs to, which are harder, rougher, more egoistic.
At about 30 points Edwin is on the way towards becoming like Chuck (to a lesser extend except playing towards that) or Kath (which in this case is likely Edwin´s mentor). He is on the fast way to become a sociopath and best buddy of Kath. Not only impcts that his inner monologue, but you loose some choice options, mainly the nice and human ones.
As some theory about some later events where toughness will play a role is if edwin stays at PC or wants out. The low T and the mischievious Edwin might stay in the Club with Hana, making some reforms. Both Edwin (and Hana) version might have some corruption (if played towards that) in how wild they are in bed and how much they enjoy partaking "owners options", but they will lead PC towards being not as big a den of exploitation as it is now. (Hana´s talk with Feli during the Saturday event is one hint, Feli is there without external pressure, that is something which Hana would want for all the girls in PC. Hana is not against sex work, but that PC exploits many who are desperate.)
The 30+ Edwin on the other hand will be quite happy with how PC currently is and gets off it being a den of vices and sadism.