It's hard to say but I don't think they're coached up to do it, at least not explicitly. It may just be a lingering bad habit from a franchise used to low defensive / hockey IQ standards for the past decade plus (thanks GMGM).
After the Tavares OTGWG in Game 3 on the heels of Carlson blindly clearing it up the boards, Trotz questioned the decision and said he had options rather than chip it up the boards. But it's not clear they routinely practice quick decision-making or pushing the pace in that fashion generally. They certainly never appeared like a team that did. Away from the puck and defensive structure seemed to be about all they really prioritized this season. The rest was left up to chance. I guess you could blame it on limited personnel, particularly up front, but that shouldn't stop them from selectively raising the bar for those capable of carrying it.
When players execute the safe chip play, coaches praise making the simple play. It seems to me it's less of an explicit directive across the board than default mode in the absence of composed preparedness. It's the panic play...effective in the short-term but it adds up in the end. It's hard to say for sure without more on the record from players and coaches but the Caps really did stick in that regard in a big way. So much money spent on the blueline yet they largely played a primitive style.
Improved forward personnel could help, esp. a couple of natural bottom six centers that can skate and support defensively. Playing faster in the regular season so they're more comfortable playing on their toes would also help. They weren't ready for resilient opposition or high tempo contests. They just kind of fought through their own self-imposed lethargy much of the playoffs and Trotz should probably look for the reasons why that was the case. They're not that hard to find.