I think it's a bit of muddle for the early period, for the 18th c. On one hand, in the pre-industrial world, land was money, the most basic source of most all wealth. Good land at a very low price was a powerful temptation to immigration ( and I say low price because, contrary to popular notions about settlers, mostly they would be buying from land speculators and/or the government) and in 17th c. England there was an over-supply of landless laborers and land-poor farmers, likewise in the Palatinate in Germany in the 18th c. Siphoning off landless farmers likely did calm things a bit in England, where common lands were being enclosed in the 16th & 17th c. And there was civil strife in some places in the colonies where land for those immigrants was in short supply: the Hudson Valley was settled quite early, and many of those early farms were very large. Immigrants arriving in the 18th c. who chose the Hudson Valley could only set up on tenant farms within those large estates, and would often discover their landlords to be pretty unbearable. The disputes between tenants and landlords there would create enough resentment that the population in many places was unwilling to follow their landlords in supporting the revolt against the British in 1775.

Likewise, the Proclamation of 1763 limited settlement beyond the Alleghenies, and created a lot of resentment among would-be settlers and, perhaps more importantly, land speculators like George Washington. That certainly boosted support for the Continental cause in the 1775 revolt. So, if the frontier was a safety valve, shutting it off certainly created discontent.

On the other hand, for most of the colonies the frontier was in the west, but the political power was retained by established elites in the east, and they did not have the same needs. In North Carolina, especially, the eastern elites would mostly ignore the west, exacting taxes but denying it any voice in the government. This resulted in the famous Regulators revolt, which ended very badly for the Regulators. And the French and Indian War came about as a direct result of settlers moving west and into conflict with Native nations in French territory.

After the Revolution, this east-west divide continued to be a source of trouble. Shays' Rebellion was a revolt of western Massachusetts farmers against a hard-money tax requirement imposed for the benefit of eastern merchants. And the Whiskey Rebellion was in many ways more than a tax unfairly imposed by easterners on the frontier: it can be seen as an expression of frontier anger at unwillingness of the eastern governments to give them their due, to defend them from Native attacks ( and, the Native Americans would have said, to defend Native Nations from settler attacks), and to negotiate effectively with the Spanish for the use of the Mississippi river system for exporting their produce.

Soon some political power would go west: when new states like Tennessee and Kentucky were formed. Whether that made the new frontier a safety valve, or whether it just created more tensions in the 19th c. between slave-holding Southerners and Abolitionist Northerners, Republican eastern elite bankers and western Democratic Populist farmers, I will leave for someone else to say.