  Compactifying the SM down to 3D or 2D one may obtain AdS vacua depending on
the neutrino mass spectrum. It has been recently shown that, by insisting in
the absence of these vacua, as suggested by {\it Weak Gravity Conjecture} (WGC)
arguments, intriguing constraints on the value of the lightest neutrino mass
and the 4D cosmological constant are obtained. For fixed Yukawa coupling one
also obtains an upper bound on the EW scale $\left\langle
H\right\rangle\lesssim {\Lambda_4^{1/4}} /{Y_{\nu_{i}}}$,where $\Lambda_4$ is
the 4D cosmological constant and $Y_{\nu_{i}}$ the Yukawa coupling of the
lightest (Dirac) neutrino. This bound may lead to a reassessment of the gauge
hierarchy problem. In this letter, following the same line of arguments, we
point out that the SM without a Higgs field would give rise to new AdS lower
dimensional vacua. Absence of latter would require the very existence of the SM
Higgs. Furthermore one can derive a lower bound on the Higgs vev $\left\langle
H\right\rangle\gtrsim \Lambda_{\text{QCD}}$ which is required by the absence of
AdS vacua in lower dimensions. The lowest number of quark/lepton generations in
which this need for a Higgs applies is three, giving a justification for family
replication. We also reassess the connection between the EW scale, neutrino
masses and the c.c. in this approach. The EW fine-tuning is here related to the
proximity between the c.c. scale $\Lambda_4^{1/4}$ and the lightest neutrino
mass $m_{\nu_i}$ by the expression $ \frac {\Delta H}{H} \lesssim \frac
{(a\Lambda_4^ {1/4} -m_{\nu_i})} {m_{\nu_i}}. $ We emphasize that all the above
results rely on the assumption of the stability of the AdS SM vacua found.
