Proton - neutron fusion?

Of course the reaction is possible. It doesn't even require special environmental conditions. Having no charge the neutrons don't need to overcome a strong Coulomb barrier to interact with atomic nuclei and will happily find any nuclei that can capture them at thermal energies. KamLAND (for instance) relies on this reaction as the delayed part of the delay-coincidence in detecting anti-neutrino events in the detector. In the mineral oil environment of KamLAND the free neutrons have a mean lifetime around $200 \,\mathrm{\mu s}$.

Neutron capture even on a proton releases 2.2 MeV. Chlorine, boron and gadolinium are all better neutron capture agents than hydrogen bearing molecules like water and oils, and captures to those absorbers release even more energy per event.

So why isn't everyone jumping around cheering for room temperature fusion and prognosticating a beautiful future full of safe and abundant energy?

Because there is no adequate supply of free neutrons. With their roughly 15 minute beta-decay lifetime there is no naturally occurring reserve and you can't store them in any case.

The p + n --> D and D + n --> T reactions are the basis of the difference between light and heavy water used as the moderator in fission reactors. Because the former reaction has bigger cross section and steals more neutrons from the chain reaction neutron economy.

Because of the optimal proton/neutron mass ratio, light water would be better moderator than heavy water, as it faster slows down neutrons to the thermal speed. It would be, but is not, as this effect is overruled by higher neutron absorption.

The result is, that while heavy water moderator allows to build fission reactors with unriched uranium, reactors with light water moderator require enriched uranium. ( typically 2-3 % of 235U, instead of the natural 0.7% )