Why are so many recreational drugs serotonin 5-HT1A partial agonists?
Interesting notion. However, the main effects of the indoleamine-class of psychoactive compounds, including psilocybin and LSD (Shulgin, 1997), are generally ascribed to 5-HT2A receptors and the glutamatergic system (Aghajanian &amp; Marek, 1999). The stimulant effects of the phenetylamines (PEAs) such as amphetamine and related compounds (Shulgin, 1991) mainly target the dopamine (DA) and noradrenergic (NE) systems. I reckon that the 5HT1A effects are 'side effects', or secondary effects.

Antidepressants, such as the selective serotonin-reuptake inhibitors,  target the 5HT1A system and mainly do so by downregulating the pre-synaptic variant of the 5HT1A receptors, which have a regulatory role by decreasing 5HT release. Downregulating them takes about 2 weeks. After that time 5HT release is disinhibited and 5HT release is enhanced, which has antidepressant actions (source: Sci Am, 2013). Because many recreational drugs are not taken that long, my educated guess is that acute activation of 5HT1A by recreational drugs limits the drug's effect more than anything else.

Why are they partial agonists? Because they target other receptors better; the main effects of e.g., PEAs as described above shows you why. Many of those compounds mainly target the DA and NE system. Because they are aspecific ('dirty') drugs, they also target a variety of other receptor systems. Perhaps altering the main effect, perhaps not doing anything substantial to the trip. 

Note that the PEA MDMA is kind of a one-of-a-kind psychoactive compound (Shulgin, 1991) that releases massive amounts of 5HT (Gartside et al., 1997).   

On a side note, Wikipedia tends to list all available information on an item in a cluttered way that obscures the relevance of that information to the global picture.

References
- Aghajanian &amp; Marek, Neuropsychopharmacology (1999); 21(2 Suppl): 16S-23S
- Gartside et al., Neuropharmacology (1997); 36(11-12): 1697-703
- Shulgin, Pihkal (1991), Transform Press
- Shulgin, Tihkal (1997), Transform Press