If you can get a clausing, get it. But the lathe is not to blame when a pin is not straight. I use a version of a taig lathe, made from parts.
Sometimes I use the steady with a precision sleeve to hold the shaft or handle, others I use the headstock. It makes no difference which you use.The important part is that the item runs true and is not strained to be in position.The taig type lathes need to be properly leveled and set up.The tailstock must be zero to the headstock. The steady must also be zero to the headstock. Finally, all 3 need to be in zero position. If not, it will not work, especially when you start to tap the hole as it will be at an angle if everything is not right.All too often people blame the arrow when it is the user. Some equipment is needed to set up a machine properly, I feel this step is often missed by lots of people who post here with issues.
If the headstock, steady, tailstock are with .001 inches of alignment,there will be very little to no run out detectable on the finished product.
Then of course it is assumed that the person doing the work knows of the method required to get the job done as well.
Just buying a clausing is not going to guarantee that the pin work will be straight either. It too will need to be correctly installed and leveled and checked for alignment.
Some times you have to shim tailstocks or steadyrests to get them to zero with the headstock. Sometimes you have to twist the lathe bed a little to get it all to align, maybe up to .010 or .020 inches. Over 40 inches or so ,it does not take much to twist .010 inches. If the machine is not solidly mounted, just leaning on the machine can cause some movement.
I know quite a few very good machinist that have never had to level a machine before, and do not have that experience.
It makes more of a difference that most give it credit.
Neil