"So let's look at it this way and let's say we do have some nearly perfect cattle to begin with. The quickest and obvious first option available is to put the bull with his own daughters, right? What would the advantages, disadvantages and possible outcome of this particular linebreeding technique be?"
If you do some historic study of linebreeding and try some you will find that about 15% or less of livestock (generally individuals or small populations) can stand that genetic pressure and do what folks want them to do. So you then have a greatly reduced genepool to start. You face a more rapid rise in the future of the %IBC.
Generally, linebreeding does not automatically eliminate genetic variations. Study the isolated populations of red deer and soay sheep. Anything but. You will continue to force your selective power on a closed population or else you will not see what you think you want to see. This will also speed the increase of the average %IBC.
If you want to know if it is going to work ASAP: son to mother or sire to daughter. The most powerful one to me: son to mother. An opinion. But you are still dealing with mitochondrial DNA transfer which is only transferred from the female which is a big plus.
Most folks do not like linebred animals. They will be deemed suspect by some. It is a modern thought as you know the way lines and breeds were historically developed. To linebreed is working against the modern marvels of buying semen, sale catalog purchases and being one of the good ol' boys. The base network of livestock production: other folks want your money and loyalty. As a linebreeder you are an outsider. There's more human issues in animal breeding than there is animal issues.
The semen catalogs and sale catalogs will highlight a bull occasionally as linebred or outcross but if you look at the actual pedigree you will see that they are not honest.
If you linebreed registered livestock you will quickly have EPDs which are irrelevant to the comparative mainstream cattle. The EPDs will grow to be quite inaccurate.