I don't think it needs to be pushed on every state that offers sheep hunts. I do think it should be considered when feasible and when the limited entry hunts aren't living up to the "as advertised". You've outlined the mindset of the vast majority of those that draw a sheep tag- they should have ample opportunity at killing a "trophy" ram. I'm by no means advocating against that. In fact, quite the opposite. 302 for example has some great trophy ram potential, and those that draw it expect to kill a mature ram, not just have an opportunity to do so. But as it currently stands, there are numerous years where the success rate is 66% (4/6) or so due to how the season is structured and when the sheep migrate to lower, more accessible country (It closes October 31st instead of the last Sunday of November like most other hunts). What I would advocate for in this case, is that you reduce the LE tags to 4 from 6, but have the season run through the end of the general season. I would then allocate the other 2 tags, or even 1 tag, to a UL hunt in the backcountry portion of the unit where no one is currently killing sheep anyway. This is just one unit, which has its own issues. My idea wouldn't work in every unit, or even most, but it could work here to both create more "opportunity" as well as to improve the LE hunters opportunity, success, and trophy potential. I think there are creative solutions that can do this across different states, Wyoming or not.
As to the age of the unlimited rams, or being "barely legal"- this will always come down to a hunters choice. I've had coworkers shoot a "legal" 150" ram in the same unit Greenhorn is hunting this year- that unit can produce 170+" rams. But it was that hunters choice. Meanwhile, hunters like Gomer and many others, have held out for the "right" ram in the Unlimiteds.
I am glad you spread your hunt out over the course of the entire season and soaked it all in. That is what makes a limited tag so special, and I would do the same if I found myself in your shoes. Meanwhile, unlimited hunters have spread their hunt out over several years or decades. That is what makes the unlimited hunts special.
I hope you aren't under the impression that I am advocating for taking away draw hunts. They have their place, for certain, and will always make up the vast majority of sheep tags. The goals for both of our mindsets are the same- quality hunts and solid herd management.