Nurses do a lot of things with stethoscope. Many pediatric RNs are good at interpreting heart murmurs; emergency nurses need to know a lot about respiration.
I would not want a generic, communal stethoscope. But I would write it off as a business expense. In hospitals, stethoscopes and decent pens are hard to find and intensely personal. Comparing this to an X-ray machine is just plain silly.
As has been pointed out, a stethoscope is as personal as your scrubs or shoes. It’s got earwax on it, for the love of god. Some things are just disgusting, even for folks who deal with blood, shit, piss, and pus all day.
Your employer is no more required to buy you a stethoscope than they are to buy your scrubs, which are often proportionately more expensive. A $100 stethoscope will see use every day for years and years, barring carelessness or outright abuse. That $25 set of basic scrubs will wear out pretty damn fast if you wear it every day. Of course, a truly nice set of scrubs is closer to $60.
The problem with communal instruments is this: they either drift away (so when you need them, they’re in some absentminded person’s pocket, or in the next room, or anywhere but they’re proper place) or they get in bad shape really quickly. Hemostats get sprung, bandage scissors get dulled (sometimes because someones been cutting paper with them), stethoscope bells get loose, etc. If you have your own stuff, you always know where it is, and you can monitor it for damage or wear and tear.
…I’ve been a critical care RN for over twenty years and have paid mucho denaro for my 'scope because I rely on it to provide competent, accurate assessments and quality nursing care to my patients. If, God forbid, the hospital bought them they’d buy the cheapest ones around, and that wouldn’t be good for the nurses or the patients.
Besides, it’s tax deductible…and when it comes to taxes my wife and I (also an RN) need all the breaks we can get. 
How’s about you do your SO a favor and buy her a good stethoscope? She’d love you forever, and that’d feel mighty good.
I would not want to use a ‘group’ steth. I like my own. I keep it clean and know where it has been. Plus, I have comfy foam eartips and extra length. There are group steths at work available, I just prefer my own.