The catholic church has always had trouble keeping even a tiny portion of its men celibate; simple arithmetic suggests that in communities where polygamy was common serious problems must have ensued.
Most (but not exclusively) interested in 19th century Mormon approaches to this problem (if it was a problem). I know the FLDS was fond of kicking out its young men for small or trumped-up offenses.
This has been asked before.
In summary, in societies where polygamy was accepted but not common, competition was kept down by a combination of
In societies where polygamy was the norm, such as pre-statehood Mormon Utah, competition was indeed kept down by expelling young men from the community.