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Interesting thought about whether they are more "relevant" if the games are OOC rivalries, or more interesting?

The only major national rivalries today that are of that ilk are ND-USC, I think.  UGA-Tech and Clemson-USC are one sided, and often not of national import.

UK-Louisville, meh.  

It's different, that's for sure.  If nothing else, it's harder to wish that Texas would lose every game they play, as that would reflect on the record of every other team in the conference.
I'm not sure it has been less nationally relevant since the Big 12 was formed.  It usually wasn't relevant in the 1960s, because Texas was good and OU was not.  And it wan't very relevant from 1986 through 1995, the last year before the Big 12 was formed, as first Texas, then OU, went through some tough years.  But from 2000 through 2010, it was nearly always for the championship of the Big 12-S, and that nearly always meant the Big 12 championship.  The lack of national relevance since then (after the Big 12 nearly cratered but stabilized at 10 teams) has been because, with the exception of 2011, at least one of the teams has had at least one loss.  Or so it seems to me.

My thinking is that the OOC games are often more nationally relevant because they tend to be big factors in determining which conference champion gets to the CFP (and previously BCS) where the conference games are more about which team wins the conference.  

As a fan of a team that isn't OU or UT, if my team is in the NC hunt, the result of OU/UT usually doesn't matter much.  Either way, some team will win the B12 and that team will have an argument for a CFP spot.  I think it is the same for most outsiders view of tOSU/M.  Either way, somebody will win the B1G and have an argument for a CFP spot.  

In that way, major national OOC games like tOSU/OU in 2016 and 2017 are a bigger deal.  Both years the winner got into the CFP and the loser did not and both years the result of that game was, at least arguably, the deciding factor.  In 2016 Ohio State was NOT a conference champion but owning a win over the B12 Champion obviously helped.  In 2017 Oklahoma was a 12-1 conference champion but they had a somewhat questionable loss (at home to a mediocre ISU team).  Their big win in Columbus over the B1G Champion helped to prevent anyone from doubting them and they got in.  

Big OOC games indeed are relevant, no doubt, even "one step away".  Let's say UGA beats ND and then loses to LSU in the CG, and LSU is 11-2, that win over a team that beat ND (if ND is in the mix) is a factor.

If Clemson is say 12-1 and ACC champ but lost at home to A&M who LSU beat, it could be a factor.

This is exactly the kind of example I was thinking of.  Back in the SWC/B8 days if Texas beat OU and aTm won the SWC with a win over UT that Texas win over OU might REALLY help aTm.  Similarly, if OU beat Texas then Nebraska won the B8 with a win over OU, Oklahoma's win over Texas might REALLY help Nebraska.  I think that the ripple effects are smaller in a conference game.  

The game I always think of in this context is Colorado's miraculous hail mary in Ann Arbor
Colorado's miraculous hail mary in Ann Arbor to beat the Wolverines.  

As it turned out, neither team won their conference and neither team ended up seriously in the NC discussion.  Colorado lost to a Nebraska team that ran the table in the B8 while Michigan lost to Wisconsin, Ohio State, and a Penn State team that ran the table in the Big11Ten.  

That said, I strongly believe that this result ended up deciding the NC of Nebraska over Penn State:

When the game was played Michigan was #4 and Colorado was #7.  That result moved Colorado up to #5 and Michigan down to #7.  

When #1 Florida lost to Auburn, Penn State moved up to #1 in part on the strength of their win over #5 Michigan but Colorado and Nebraska were 2/3 and had yet to play each other.  Penn State was doomed.  A few weeks later Nebraska beat #2 Colorado and moved up to #1 despite the fact that PSU annihilated a ranked team (#21 tOSU) that same week.  

If you flip the Colorado/Michigan result I think that Penn State holds on to #1 because Nebraska's win over the Buffaloes wouldn't have been as impressive.  

Therein lies of course the issue with how rankings happen, a team you beat might lose one on a miracle and it hurts your ranking and perception.

We often see some 7-2 team ranked say 12th lose a close game on the road to the #3 team and DROP to 16th at 7-3, or lower.  Or conversely, they win a game on a miracle play and suddenly jump to 6th on the basis of beating that #3 team which then goes on to lose 3 more games and drops out, but folks forget, somehow.

Syllogism, it really doesn't work well for rankings.  And it remains an issue that beating a team ranked say #5 early does you more good than if they have faded to unranked and you beat them late.

Yes, the could have had injuries, often as not they were over rated early.  Beat #3 early as a #18 team and you will vault to #7 or so and stay even if the #3 ends up 7-6.

Having the committee not rank, or announce anyway, until later is a good thing.  Maybe that win over #3 was good at the time and they lost their QB.