Dodge trucks are notoriously sloppy. Some blame a poor frame design in the front which flexes too much, others blame dropping in a heavy diesel engine into a front end that is not that strong, the opinions are endless. I will say that I used to drive an early 2000s 2500 gasser for work and the steering was just about as bad as my 2001 CTD. However, I digress. I just looked at my steering shaft and it looks exactly like yours, although a bit dirtier. If I were you, I would go on Cummins Forum and read up on the steering improvements. Here is my general synopsis of reading many posts from there, as I am hopefully going to redo my entire front end this year:
1) Improve the steering by adding steering support brace. Many companies essential make a brace that ties the two frame rails together (commonly called the BD Brace) that will improve the steering. Downside is that the frame rails are tied together and steering components can be damamaged because of the reduced flex. Supposedly, the Dodge Off Road brace eliminates this and this is what I plan on purchasing (there are threads on both Cummins Forum and ExPo about the DOR brace)
2) Upgrade the steering components by buying the Mopar 4th Generation steering kit. Do a search on Cummins Forum for this and you will get the Mopar part number. It is about $250-300 and it is all of the major components to upgrade the steering from a Y linkage to a T linkage. Supposedly, it vastly improves the steering and, again, it is what I plan on purchasing. There are also many aftermarket options to do something similar, but for the ease or part replacement in the future, I like OEM. I believe you can also swap in 3rd Generation gear to improve the steering, but supposedly the 4th generation is much stronger (larger, thicker tubing, etc.)
3) Upgrade the steering box. Redheads are highly recommended, although I recently read about a larger box from Borgeson I think? I'm not quite sure of that, but the Redheads seem to get good reviews, although I have seen some unhappy reports.
4) Upgrade the track bar. Again, take your pick of beefed up aftermarket or an OEM track bar from a 3rd or 4th generation Ram. I believe the 3rd generation is a direct bolt on swap with no modifications but the new bar has stronger tubing. Some of the aftermarket track bars are adjustable and others swap out the weak tie rod ends for stronger and more durable heim connections.
5) Upgrade the tie rod ends and bushings. Lots of aftermarket discussion on Cummins Forum. Moogs and XRF are highly recommended for TREs.
6) Install the Rock Solid Ram steering column bushing to replace the lower steering column bushing. There is not as much talk about this on Cummins Forum but it seems like an easy improvement that is cheap and from what I have read on the forum it seems to help. My steering is starting to make a rub noise when I turn lock to lock and I believe it might be a worn bushing on the column.
Okay, so I think that is my summary of my research so far. My general plan this year is make most of those improvements as time and money allows. My guess is that on your truck you are starting to feel the wear from worn out TREs combined with the sloppy original design and possibly some wear in the box. My guess is that your spline and pitman arm are fine.
Good luck and let us know how it goes.