Use this when you must decline a request, refuse a condition, or say something is outside what you can do, and you want maximum politeness and distance — it softens a flat 「できません」 into an institutional "I am regrettably not in a position to." It is standard in customer replies, negotiation emails, and formal notices, and is far more common in writing and scripted service speech than in casual conversation. Note the contrast with 〜かねない ("may well happen"): 〜かねます is negative-in-meaning despite the affirmative-looking form.