This is an addendum to Jason's answer.

Mueller [1] and Lapid-Mueller [2] have exploited Arthur's trace formula to come up with a **Weyl law** for GL(n) with an excellent error term. (Their method has been adapted by others, Matz, Matz-Templier etc.). Since they are counting all automorphic representations (with a fixed infinitesimal character), the simple trace formula simply cannot detect them.

Much more importantly, Arthur's trace formula has been an indispensible tool in proving important (endoscopic) cases of **Langlands' functoriality** which hasn't been done (cannot?) by other trace formulas. We now have functoriality so far for classical groups, unitary groups, their inner twists, spin groups.

Nevertheless, Labesse-Mueller proved a weak Weyl law and also Kottwitz could prove the Tamagawa number conjecture (see Jason's answer) using weak test functions in Arthur's trace formula.

[1]: Mueller, Weyl's law for the cuspidal spectrum of $SL_n$

[2]: Lapid-Mueller, Spectral asymptotics for arithmetic quotients of ${\rm SL}(n,{\mathbb R})/\rm{SO}(n)$

[3]: Labesse-Mueller, Weak Weyl's law for congruence subgroups