Realistically, only so many primo tags and not enough to meet demand. As you have learned, each state has its own approach where it allocates the tags to perhaps outfitters, non-profits, commissioners, residents and non-residents.
If you are looking to go on a rut hunt with large animals and high harvest rates then in most states you will only draw a coveted tag once every 10-30 years. That is 1 to 4 times in your hunting life.
States with preference point systems on species face point creep on the primo tags. If it take 10 points to draw Unit X this year, may take 11 next year rather than 10 so you are only very slowly getting closer to having enough points to draw that tag as the years pass. Colorado is attempting to deal with that with the hybrid approach to deer and elk. Wyoming sheep tags will soon be going to mostly 70 year olds too old to have much success on a rugged sheep hunt.
Idaho and New Mexico do not use points so you might draw first year.
Nevada is example of state that uses bonus point system so the sooner you get started the better since they square your points to decide how many chances you have in each draw.
Some states like Wyoming use a blended approach so you might draw a tag first year if very lucky but most tags go to max point folks.
I apply for 70 tags a year in 10 western states and have never drawn more than 3 and some years have drawn just 1 tag. I apply for only primo hunts with odds as tough as 1:4000 and usually not better than 1:40. If I was applying for tags with 1:4 odds then I would never attempt 70 draws, though.
Is not a cheap hobby. I spend about $2000 a year on fees and licenses just to enter the draws and tie up a lot of money when have to prepay the entire tag amount to apply. The amount I spend and tie up each year is going up since states are raising fees much more than inflation. Take Oregon, if you want to hunt pronghorn as non-resident then might spend $2000 by time get drawn ("less" if apply for multiple species in Oregon since can spread the $2000 around sheep, deer, and elk draws, too). You can get a nice landowner pronghorn tag this year in NM for $2000. I will burn my Oregon deer points this year and elk next year then am done there based on my view of the game quality vs. cost to keep applying.
If I am skunked on all 70 draws one of these years, my Plan B is to pick up landowner tag in NM or CO or do OTC hunt.
Good luck and someone has to draw so might be you.