Entirely depends on the semi-auto at hand. Some just are not going to be bughole rifles no matter what you do. Some can get there with simple load development. Some take a little more effort. A decently made AR platform with a free float upper can usually be made to be sufficiently accurate for the task. I've never been able to get a BAR (the hunting rifle, not the machine gun) to be accurate enough for the task.
I got my Aero M5 308 build as accurate as my Ruger Precision Rifle in 308. Sold the RPR. If it works, then it works. I think to many people discount this and just want to run the status quo in fear of being mocked.
I have a BAR in 300 win mag that I gave my dad a long time ago but he quit hunting he's 81 so I am about to use it .I have shot alot of 1/2 inch groups and some 3/8 inch groups with this rifle at 100 yards with just a 3x9 Nikon on it . You have to keep the bore clean to make it shoot like this with good loads and clean it every 50 rounds and pull a bore snake through it .I am thinking about putting a 6x24 x50 Nikon mrad scope on it to see what it will do long range . We only shot deer with it out to 300 yards but I bet with today's bullets it will be easy to become a 500 yard rifle .I also have a rem 742 in 243 win that shoots 1/2 inch at 100 yards and have shot lots of 1 inch groups at 200 yards .These rifles were both shot with factory ammo so good reloads would probally do just as good .I forgot I also have the most surprising accurate semiautomatic a ruger mini 14 target rifle in 223 it shoots all day 1/2 groups at 100 yards and 1 inch at 200 yards with a 6x18 power scope on it .
I am a fan of the semi auto platform for precision shooting within the capability of the cartridge it's chambered in. I shoot a 308 AR, it's one of my favorite rifles to shoot. It has a 18" Rock Creek 5R barrel and with a can it's very enjoyable and capable of the accuracy needed to get consistent hits out to 650yds.
Beyond that, I would move probably move to a magnum bolt action. I live in WV, where finding a clear shot beyond 650yds is not so common. Shooting 650yds here, 800'-1000'ASL in 60-80%+ humidity with thick forest and vegetation limiting shots makes it a challenge vs shooting wide open shots at high elevation at the same range. So for me, in my area, it works perfectly. To folks out west that isn't even considered long range, more intermediate.
So I think they have their place. I've never fired a Nemo Omen. They are chambered in cartridges that have the ability to get to longer ranges. I've found that semi autos limit the load due to the gas system. But I am a believer in the AR platform when built properly, can produce the accuracy to get out there. So I vote yes...