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In the context of atomically precise manufacturing in general and and gemstone metamaterial technology in particular hydrogen basically acts like a plug for open chemical bonds (a plug for radicals).
This is what makes it very useful.

While there are limits of construction kit analogy for the periodic table of elements.
Viewing hydrogen hydrogen atoms as "plugs" is still a very good first approximation for many cases where one would want to use it in. One just needs to be aware of the cases where it starts behaving differently. Like e.g. in conjunction with electron deficient atoms like boron and aluminum (or much of the left side of the periodic table, center being the carbon group).

Halogens as alternative "bond closing plugs"

Halogen atoms (which hydrogen is sometimes grouped to) can often be used similarly.
They also prefer a bond order of one. Bigger heavier ones less so.
To note is that halogen containing materials can release for health and environment problematic substances on combustion.
Combustion of PVC can e.g. produce phosgene. Fluorine also nasty stuff.
Many gemstone like material are not combustible though. Including moissanite (SiC).
Also the fraction of halogens is expectable to be low. Se below for why.

Especially chlorine is highly abundant. Fluorine so-so.
The other ones bromine and iodine are rather scarce.
Nit to speak of traces of the the extremely radioactive element astatine
(with a metallic chemistry similar to silver according to wikipedia).

Hydrogen in advanced gem-gum technology and manufacturing

Use as nanoscale surface passivation element

Hydrogen is useful for nanoscale passivation of the surfaces of crystolecules.
In particular useful for the passivation of diamond, lonsdaleite and other sp3 allotropes of carbon.
Also for the passivation of Moissanite (SiC) and maybe pure silicon.

For sliding interfaces atoms with a bond order of two (namely the chalcogens: oxygen and sulfur and maybe selene)
are likely better since their bond geometry strongly suppresses snapback.

Many interesting gemstone-like compounds may not be well passivatable by hydrogen.
These may either use other means for passivation or avoid use cases that call for nanoscale surface passivation.

Assembly and disassembly as individual atoms

Hydrogen is one of the few elements that are really handled as individual atoms and not
partially hydrogen passivated minimal molecule fragments.
Other elements for which that may hold to are perhaps:

  • lighter smaller halogen atoms like fluorine and maybe chlorine -- these to prefer a bond order of one
  • heavier bigger noble gas atoms that are at leas somewhat reactive -- these need low temperatures and highly reactive partners to react at all

Low demand for hydrogen compared to other elements

Compared to hydrocarbons in plastics crystolecules have much less surface area per internal volume. With hydrogen mostly being on the surface of crystoleculed the quantity of necessary hydrogen is thus small compared to the elements inside.

Hydrogen in earlier forms of atomically precise manufacturing

Virtually all foldamers contain plenty of hydrogen as nanoscale passivation.
There are only a very few hydrogen free anorganic polymers that do not fuse together to a dense 3D network of bonds.