There are at least two ways to redistribute and homogenize a mixture of solids and liquids: physically redistribute the solids (mix and stir) or redistribute the liquid.
Physically mixing and stirring mash in a tun is pretty difficult and probably uneven, even with the best rake or stirring system. It's downright poor with just a paddle. Pumping the wort through that mash is a lot easier and more effective (as long as the flow distributor and collector system are well designed).
I went to a RIMS for my brewing over 20 years ago and haven't regretted it. About 6 or 7 years ago, I finally accepted and understood that avoiding oxygen contact with wort was the secret to producing the malt character that's found in good commercial German lagers and I implemented a mash cap system that significantly reduces that air contact. That factor is a serious reason to consider RIMS since any sort of stirring at the homebrew level is likely to introduce a lot of air contact to the grist and wort. While I agree that LODO isn't appropriate for all beer styles, it can certainly make a difference in some.
I recirculate constantly with my RIMS and I've wondered if that is 'tearing up' my wort and causing problems like reducing the length of protein chains. I think my beers still have body, so I don't think that occurs. If someone has a differing opinion, I'd like to hear it.