What about the hidden cost of materials you ruin when a patch job fails mid-cut? I've seen guys waste expensive hardwood because a patched guide bearing locked up. That lost lumber plus downtime often costs more than the replacement part. For small shops, that unexpected loss can really hurt the next job's budget.
People patch stuff all the time and it works out fine. A snapped chain sounds scary but it's not always a huge deal. Maybe just get it fixed and keep a closer eye on it.