Plenty of units in Colorado are easy to draw without points and some even offer OTC after all the draws are complete (at least this was the case when we drew 2017 without any points). All 3 of us drew Colorado without any points. We were told near 100% draw rates...not sure if we lucked out or not but we hunted nonetheless.
Montana is where we are going this year and it too seems to be fairly easy to draw. We knew we were going last year so we bought a preference point last year and bought another this year and applied. They allow you to buy a point and apply for the draw in the same year...basically we had 3 points going into the draw doing this. If you apply as a group supposedly your odds are better too...again is that true I dont know but it worked for us. The way I understand the combo elk/deer tag in Montana is that you are not awarded based off the number of points you have, just simply the more you have the better the chance. Anyways not sure if we needed to do this but all 3 of us drew without issue. A small amount to pay for added guarantee of getting the tag.*
Im not sure about other states but Id assume most are like this and probably pretty much any you could get a random cow tag if you wanted to just do a meat hunt. The higher the likelihood of having greater opportunity at a bigger bull the more points you will need to have so if you want to eventually hunt a trophy, no harm in starting to build those points now. Some can take upwards of 10+ to get a shot.
*Disclaimer, the guide we are going with employees a lady to do all the tag work for their hunters. All statements about Montana were based off memory of what our guide/tag buyer said since we physically didnt apply on our own so I could have misspoke