  Recent results have generalized Gowers' Theorem (to Lupini's Theorem) and the
Furstenberg-Katznelson theorem, both infinite dimensional Ramsey Theorems. The
framework of arXiv:1611.06600 provides a machine which accepts (almost
$\mathcal{R}$-trivial) monoids and outputs Ramsey theorems. The major
generalization was to extract monoid actions from these theorems.
  We investigate the other direction, and feed into the machine monoids which
appear "naturally", and which are not extracted from a Ramsey theorem, such as
such as $0$-Hecke monoids and hyperplane face monoids. Most examples of monoids
coming from geometry will not be Ramsey monoids. We provide a simple
combinatorial condition for checking this that goes through the representation
of almost $\mathcal{R}$-trivial monoids as a family of (almost) regressive
functions.
  Except in extremely small or trivial cases, the naturally occurring monoids
will not be Ramsey.
