We've switched from 2.7 to 3.4 (and upwards to 3.5, 3.6) in about a month or so. It delayed some deployments but nothing serious.
If you do it step-by-step it's not that hard. The worst part was str/binary conversions but afterwards everything was a lot easier and better to maintain.
If your company is big enough you should maintain and keep it up-to-date, not "it just works"(TM) and hope for the best after 10 years. The death of 2.7 was already in the air for years.