I know, I was also at that match, and happen to know the 3rd place winner.
Sure, you can win a match with an AI or a PGW, etc. but it's not the best tool for the job. Their chassis weren't designed with shooting off of barricades in mind, and although they can do it, they do not excel at it. There are work arounds as well, such as using the RRS SOAR products, which make some of these rifles more effective at PRS type shooting.
I happen to live in Texas and as a member of TxPRC, and have shot in a bunch of the local club matches (along with 3 PRS matches this year). These club matches are attended by a lot of AI shooters. AI rifles are really popular in Texas, especially South Texas due to Jacob Bynum of Rifle's Only, but guess what rifles are consistently at the top of the leaderboard? Almost always a custom rifle. One of the top shooters does use an AI AT (he's also a fairly highly ranked PRS shooter), but he cut his stock skins and chassis to create a 90 degree ledge in the front of the magwell to make it more effective for barricades. I also have a friend who is from the UK who I have trained with at Rifle's Only and K&M at their signature 4 & 5 day precision rifle courses, and he is strongly considering selling his AI rifle to build a custom rifle for this type of shooting. A custom rifle will cost a lot to ship and import to the UK (will end up costing thousands more than an AI), yet he see's a definite advantage to custom rifles than to his AI, so it's worth the additional cost. Sure these are all anecdotal examples, but so are yours.
Can you win a match with them? Certainly. Is it the best tool for the job? Probably not. If you are somewhat experienced and have an idea of what works and what doesn't work for your shooting style, you can get a custom made rifle which mates up perfectly with you and your style of shooting. If you are rather inexperienced and just getting into the game, then perhaps just getting a factory rifle is the best option for you as you don't really know what you want/what would work best for you anyways. The bonus with a factory rifle is that the resale is generally a bit better than a custom rifle, so you'll get more of your money back when you decide to sell it to custom build a rifle that fits you.
None of those rifles are bad by any means, not at all. But if someone asked me for a recommendation for a rifle dedicated to PRS style shooting, none of them would be on the list. The OP also wants a .308, which I think is a great caliber and a lot of fun, but also not the best tool for the job for PRS type shooting.