This would be a severe unbalance, particularly to the tanking classes.

As things stand now, here's how they tend to rank in situations where an 8 person party has both a PLD and a WAR.

Defense

In general, a PLD is best for fights where there is a high level of consistent damage. This is due to longer, more powerful cooldowns and the Shield providing free mitigation irrespective of the Parry stat.
In general, a WAR is best for fights where there is spike damage at predictable intervals. This is due to Inner Beast, which can be saved for every spike provided there's a sufficient length of time between them.

Conclusion: Throw a WAR at Twintania and other similar fights. Throw PLDs at tough fights where no tank swapping is necessary(except for T8, where WAR MT damage helps). Throw both at everything anyway

Offense

In general, a WAR will do more damage than a PLD while they are main tanking something. This is mostly because of Unchained giving the ability to negate Defiance's damage penalty at pretty good intervals.
In general, a PLD will do more damage than a WAR while they are off tanking something. This is pretty much guaranteed if an MT WAR is keeping Storm's Eye up. This is because a Sword Oath increases a PLD's DPS beyond removing the penalty from Shield Oath and their possession of two of the most powerful off GCD attacks(potency wise) in the entire game on such short cooldowns.

Conclusion: If damage matters so much that you need even your Tanks to optimize for it, it's best to go WAR MT and PLD OT.

Hate Generation

In general, a PLD has a higher consistent level of hate generation than a WAR in long battles, but lower burst generation.
In general, a WAR has better burst threat than PLD, but somewhat lower levels otherwise due to the expectation that Maim and at least one Storm is to be kept up at all times.

Conclusion: An equally geared pair of tanks both trying to produce maximum threat will likely switch off at semi-regular intervals throughout a longer battle.

AOE Tanking

A WAR is better at holding hate against multiple enemies than a PLD.
A PLD is better at holding hate against a single target than a WAR.

Conclusion: It's best to send a WAR after large groups of adds while the PLD keeps the main boss busy.

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So, the main thing here is to note that each of the jobs has their things that they're best at. The significant detail to note, however, is that despite the "PLD is best at this" and "WAR is best at that", both jobs can run off and do pretty much anything the other job is considered to be better at and still succeed. What does this mean? It means that there's a good level of balance between them. This is a good thing.

This proposal to make Sword Oath even more powerful breaks the balance in the Offense section. Whereas most parties of 8 would like there to be both a PLD and WAR present, the following would occur instead of a PLD OT became even more powerful. If we imagine fights where the following is true:

A WAR is the better MT: No change.
A PLD is the better MT: Drop the WAR and get another PLD.
It doesn't matter what Tanks we have: Get two PLD's.

In short, this may recreate the 2.0 situation in which people wanted PLD's far more than they wanted WAR's, and that is bad.