Although I can provide oversize bearings and other "major turbo parts" as needed and on request, the primary intended use for my Dieselicious turbo upgrade/rebuild kit is preventative maintenance.
I do not advocate the strategy of "waiting for a wheel to hit a wall" or for some other major failure before rebuilding. By instead regularly replacing your turbocharger's bearings and seals every 100k miles or so, you will help keep your turbo performing reliably for many more miles to come, and will considerably extend it's useful life.
By replacing old worn, soft bearings (frequently made using brass!) with fresh new parts routinely, the shaft play will in fact become drastically reduced. This is because the bearings are designed to be sacrificial and take the bulk of the wear in a healthy turbocharger. The shaft (stainless steel) and housing bore surfaces (often high nickel cast iron/stainless) are considerably harder, and thus much slower to wear.
Keeping the rotating assembly tight by routine replacement of the bearings makes the seals work much more effectively. The turbine side seal in particular plays a very important role of keeping the hot, sooty, pre-turbine pressurized exhaust gasses away from the bearing area. When shaft play becomes excessive and/or the seal get worn, the pre-turbine exhaust gas blows past the seals and bearings, depositing abraisive soot/coke in the area and increasing the operaring temperatures, drastically increasing the rate of wear and causing a vicious cycle.

Turbocharger rotating assemblies, like crankshafts, do not need to be rebalanced unless they are machined. IMO, it is not a good idea to grind the shaft unless it is excessively worn, because of the added cost and complexity of the labor to do the grinding and rebalancing, and also the important fact that smaller diameter shafts are structurally weaker, allowing the rotating assemblies to vibrate more. Needlessly oversizing the bearings of a turbocharger cuts short the turbo's ultimately usable lifespan. Often the rotating assembly and bearing housing can only be oversized once before no more oversizes are available, at which point the turbo's becomes a paperweight.
By rebuilding a turbocharger themself, a do-it-yourselfer can save hundreds of dollars even if it is necessary to hire a professional to do shaft grinding and balancing. Not to mention by doing it oneself, care can be taken doing things a professional will skip, like cleaning the wastegate's valve guides to reduce friction and hand-lapping your wastegate valve into its seat (on some internally wastegated turbo applications) to restore like-new wastegate performance.