Cartridge RHF4H 14411-VK500 VN3 Nissan YD25DDTi

Can I get a new turbine wheel, slap it on, rebuild the turbo then get it balanced?
Obtaining a new turbine wheel/shaft will not solve your problem. You need a new bearing housing where the bearings are seated. Your turbo will not survive with improper external bearing clearance. You may also need to replace the turbine wheel/shaft if any damage or excessive wear occurred there.

What could make the bearing fit into the housing so loosely?
Hot shutdowns cause extensive deposits of carbon and shellac on the turbine end. As the deposits break up and flow in the oil they score and wear the bearing bore, bearing and shaft journal. Fine contaminants will score and wear virtually every bearing surface in your turbo while the larger particles will usually confine the damage to the journal bearing on the outside, such as in your case.

What other benefits do turbos have?
As well as increasing power, turbos increase torque – an engine’s strength – particularly at low revs. That’s useful in small petrol engines which tend to produce not much torque at high revs without a turbo. Naturally-aspirated diesel engines, by contrast, produce a lot of torque at low revs. Adding a turbo amplifies the effect which is why turbo diesels feel so strong if you floor the throttle at, say, 50mph in top gear.
Turbocharged cars also have quieter exhaust pipes. The turbo effectively reduces the amount of gas coming out of the exhaust, so it’s not as loud as a non-turbo car. You might hear a ‘chuff’ when you take your foot off the throttle, though. That’s the ‘wastegate’ which expels excess gas from the turbo when it’s not needed.