I've seen this pop up at more than a few events during my visiting and ACE Team tenure, and realized that most facilities' opinions don't match up with mine and what I've taught my radar students over the years. I've long been a proponent of initiating the radar handoff process on departing aircraft sooner rather than later. More often than not, this is in order to reduce eventual workload down the line.
When I get busy, I'd rather flash early rather than flash late so that transfer of comms can be completed with enough time that the Center can keep guys climbing. In a lot of cases, I've witnessed the opposite, where a late handoff results in a plane unnecessarily leveling off at the top of the TRACON before the Center can start talking to them. That being said, I thought I'd raise the discussion here.
IRL, TRACON departures nominally begin automatically flashing to the appropriate center sector within a handful of miles of the departure end of the runway (or other, computer specified distances from the departure airport). It varies, but the aircraft is often still fairly low to the ground relative to the top of TRACON airspace, and often 20 or more miles from the lateral boundary. Just because the track is flashing to you doesn't mean you have to take it.
So here's my plea to all the center guys (and to borrow a quote from my friend Nate Johns): "There is zero reason to actively reject a handoff for "flashing too early." Zero. Heck, its not even possible from the center IRL.
Why would you make more work for your compadre? Heck, why would you make more work for you? If you're not ready to talk to someone yet, just wait until you are ready, then take the handoff at that point."