The US risked substantial territory without any evidence that settlement was advanced in the slightest. Indeed, the wave which established Alabama, Mississippi, Indiana, Illinois and Missouri shows clearly that the Native Americans simply could not stand up alone or even offer a credible attempt and only active British support, which the US declaration of war provided, could give the Natives a chance to win.
Perhaps this was due in part to the fact that so many NA warriors were killed during W1812. Besides Prophetstown, there was no great American attack on the Native Americans during W1812 that was not covered with the excuse of going after either Britain or Spain. Possibly, even, active British support led to the Native Americans falling apart. If thousands of Great Lakes tribe NAs had not fought with the British, they would not have been killed, nor given the false hope of Michigan territory, and most importantly, their important leaders would not have been killed.
Furthermore, without Jackson leading the drive in the south, the Creek civil war would have been brought to a quicker and slightly less bloody end, and without American involvement the most likely outcome is a Red Stick victory - so Tecumseh now has an ally in the south.
Even if there is no US declaration of war on either England or Spain, probably both would still supply the NAs with guns and gunpowder. If the Native Americans can even partially unify before the decade ends, they could be strong enough militarily (and the Americans weak enough - without war as an excuse their peace-time army at this point was a 4-digit number) to prevent massive settlement from the SW corner of Lake Erie down the Wabash, along the Mississippi and then Tennessee, and in most of Alabama and Mississippi territory. How long this could hold for is debatable, but it certainly would be a credible attempt and it would delay westward expansion for possibly multiple decades.