If a crank came off my bike three days after I bought it, I would absolutely take the bike back to the shop and make them fix it.
If I had a series of problems with mechanical work done by my LBS, I would talk to the manager about it, and if he did not respond appropriately I would escalate it to the owners. Even if I never return to that shop again, they need to know that their sloppy work is endangering their customers.
The people who run my LBS put a premium on customer service. It's the reason I travel 20 miles to their shop, passing plenty of other shops along the way. A few years back their mechanic broke my front derailleur while adjusting it. It was a Tiagra that never worked right, so there was probably metal fatigue from too many adjustments. But the mechanic apologized and replaced it for free -- with an Ultegra.
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles