It's totally realistic...I've done it several times for $1000.
NM $550, Utah $613, CO NR elk still $800, WY general tag $707, OR $588, ID $800ish, WA $600ish
Split gas with buddies.
I've pitched a 6 man family tent that we've owned for 10+ yrs, and shared a buddies tent other years...again all items we already own for camping with family back east.
No I don't hunt elk with binos...and as I mentioned I already have a bow/arrows/rangefinder and all my camo for hunting deer & turkey in IL.
Yes - pack cooler and frozen leftovers at home...food doesn't have to cost a penny more that being home that week.
If a local comes to me with $1000 and crazy F'ing desire to hunt elk with their bow - it will absolutely happen that fall. I've taken 10+ guys from my hometown over the years on this same plan/budget.
I've also driven out and hunted solo - slept in my car - ate out of my cooler...shot the biggest bull of my life, packed it out solo and was back home round trip in 4 days. It's an absolute addiction.
If you want it bad enough you'll find a way...otherwise it's easy to make excuses.