The lead that is present in the structure of the zircon structure can thereby be assured to be radiogenic (decayed from uranium).
True ... to a first approximation. But that's not good enough for today's scientists, for whom sub-1%-accuracy is where it's at. A very small amount of lead does get incorporated in zircons at formation. Correcting the results for that small amount of initial lead is routinely done, usually based on the amount of Pb, which is not radiogenic and therefore is initial (addition of lead after formation is unusual enough to be ignored). There are also methods that don't depend on sup}204Pb.
Of course, the correction is always many orders of magnitude smaller than that needed by creationists to validate their fantasies.
I don't believe plain old U/Pb dating is a commonly used dating method today.
I'm not actually in the field, but I do follow it. Depends on what you mean by "plain old U/Pb dating". There's lots of methods involving U-Th-Pb. U-Pb concordia-discordia dating, first developed around 1954, is the preferred method. It's very accurate because the decay constants of uranium isotopes are known more accurately than any others, and it is mostly used on zircons in which the initial lead content is essentially zero because of the physics of solidification. And even that tiny bit can be corrected for in various ways. No other method can get sub-1%accuracy.
There are four stable isotopes of lead (stable meaning they don't decay, and isotopes meaning they are the same element but with slightly different numbers of particles in the nucleus). Lead-206 is produced (on Earth) only by the decay of uranium-238. Lead-207 is produced only by the decay of uranium-235. Lead-208 is produced only by the decay of thorium-232. Lead-204 is not produced on Earth; the lead-204 we have was all here when the Earth formed. (All the isotopes are formed when stars blow up).
There are many different dating methods involving uranium. The most commonly used is concordia-discordia dating. This is almost always performed on zircons. Zircon is a mineral that easily incorporates uranium when it solidifies, but lead just doesn't fit in when the zircon solidifies. So when a zircon forms it has a little uranium but essentially no lead. (This is acknowledged by the few young-earth creationists who have a clue about how the method works). Therefore any lead we see in a zircon today is due to the decay of uranium after that zircon solidified, and we can use that knowledge to determine how long ago the zircon solidified,