I don't think it's fair to lump everyone with "Larger then stock tires" into the the same group. As mentioned the amount of back space will play a huge role in how a truck rides and responds to every crack in the freeway. There are two many factors to figure in, to narrow the list of problem causes. People that run larger tires also usually have a modified suspension, lifted. Also the larger the tire the more if weighs, mud type tires can easily weigh twice what a stock tire would. That is a huge change to double the weight attached to the end of a axle! People that have lifted trucks and or larger tires also seem to play harder and dirtier then others. This along with a suspension that is struggling with more leverage and weigh, will wear much faster then a truck that only commutes every day to work on a paved road.
The tires obviously play a part in contributing to the ride and handling of any truck. But I think many owners are also to blame for much of there problems. I see trucks all the time that have very obvious front-end problems, some have larger then stock tires, while other don't. Parts wear and in time need to be replaced, shocks fail, ball joints become lose , tie-rods get sloppy and bearings don't last for ever. Also the steering box wears, when this happens you will notice alot of "Sloop" in the wheel, a dead space when the wheel is turned from right to left. There is an adjustment that can be made to correct some of this, it's as simple as turning in a screw on the steering box.
I have a 3500 with over sized mud tires, both BFG MT's and Trxus M/T's. The two sets of tires could not be more "UN-alike" then they are. The BFG's are made of a very hard rubber compound, the sidewalls are extremely stiff and barely show a bulge when running low (10-15) air pressure. On the road they have a firm feel with a stiff ride, noise is noticeable and highway bumps and cracks are felt. The Trxus tires are very,very smooth, they are made from a very soft rubber compound that soaks up every pot hole and crack, the ride is excellent. Noise is also much less with this tire, to the point of not hearing them period, they have a very aggressive tread, but no thumpedy thump while driving. Point is both tires are over sized, very heavy and both have a very aggressive mud type tread pattern, but neither one poise a steering problem. My truck does not wander, pull, shimmy, or wobble,so if mine drives fine others should be able to also. I also have a Ford that runs a very large tire, it to drives fine but not near as well as the Dodge. I think there are 3 or 4 areas that might get overlooked that can help most keep there truck driving straight and wobble free. First the front end has to be mechanically sound, nothing can operate like it was designed to with worn,damaged, or bent parts. Tires have to been in balance, the importance of that balance becomes magnified when oversize tires are used. A good, first run, quality tire will need 2-3 onces of weight to balance it out. I have seen tires that were over a pound out of balance, thats 16 ounces! That much weight is all but impossible to ever achieve a good balance, and should be returned to the manufacturer. Also be careful where you buy your tires from, many "GOOD DEALS" are not so good, tires are made in lots of 50,000 and a 10-15 % blemish or out of standard (balance) rate is not unusual. These seconds, Blemished, less then perfect tires are sold as lots, and show up in many parts of the country as unbelievable sales, or once in a life time deals, they might not be such a good deal. Balance is important, and should not be skipped then the tires are mounted. There are also companies that make balance beads that go into the tires and others like Centramatics that make balance rings that mount on the studs, both seem to make a difference. I use the Centramatics, and when combined with the normal balance, make for a very smooth ride. Next would be the importance of the steering stabilized. Most Dodges come with a small factory steering stabilizer, but it is marginal at best with stock tires, when large meats are used till becomes useless. Rancho, Tuff Country,Skyjacker all make good steering stabilizers, I ran a single Rancho for a while then switched to a Skyjacker dual in-line unit, the difference was very noticeable and I feel part reason for my good steering effect.