Right - that is the bolt face lapping tool, not the bolt face cutter. I suppose a guy could use the lapping tool for a long time to do the cutting, but I start with the cutting head, then clean it up with that lapping tool. As I said in my post above - that lapping tool you linked is the last step in a series of blueprinting steps to bring the receiver and bolt face dimensions together.
And again - if your threads and receiver face are not true to the boltway, you will do nothing to true your bolt face to the boreline - you’ll be lapping an angled face on what might already be a true face. You will do more harm than good if you simply buy the last link in the chain and pretend it is doing the job.
As I mentioned, I own these tools, and have used them. I certainly would not waste my time to lap (cut) the boltface without truing the receiver face and chasing the threads to true the receiver. The lapping spud you linked squares the boltface to the receiver face, if your receiver face isn’t true to the boltway, then having the boltface tried to the receiver face is wasted effort.