I've seen that some of the tappet covers have a breather on them. Mine has a little box the sticks out near the back, with a plate there on the inside. No clue on the purpose of that. But just wondering if there would be any reason to add a breather there like some have

You're basically covering up a piston ring(s) issue, typically or bad tuning. Why?

Well, normally, these trucks will not produce excessive crankcase pressure or blowby gases. Now, someone who runs worn injectors, then your timing could be advanced by the weaker springs in the injectors. Now, you're creating this extra blow by. might see more slobber of oil out of the crankcase vent (gear case vent). I suggest keeping injectors changed out at 100k miles. After that point your rolling the dice. For every 10 bar of pop pressure loss is about 1 degree of advancement. If your injectors haven't been changed in over 100k miles, I'd start there. Yea,h sadly, the only reason I know to add more vent/filter to the valve cover is that the factory breather is not keeping up because of the vacuum line disconnected (added pressure from the vacuum pump), poor rings on the pistons, worn injectors with low pop pressure (less than 293 bar).

Now, like Thor, I have a bad ring in Thor, and Thor starts and runs, but the exhaust is white smoke from the low compression, and there is extra crankcase pressure on Thor from the blowby, and the blowby isn't bad, but still it would help to have an extra vent at that point, but... Better to fix the problem. Yeah, I've got plans to rebuild that 2006 in the future. First problem, I need a shop to work in once again.

Another trick is you could create a vent pipe to keep the slobbering down some. Remember, this will not fix excessive blow-by.