I fail to see a reason why one should not. Some seven or so years have passed since the inception of the idea of DevOps, and the amount of evidence of its effectiveness has been growing steadily. Having the respected Agile framework at its base further adds to its credibility and perhaps helps explain a good part of its success.
That is not to say there are not considerations to be taken into account however. The critical thinker within you, would want to ask a question or two prior to embarking on such a cultural coup d'état.
Did you just finish adopting Lean or Agile Development? What else has been going on in the team? Is now the best time for yet another cry for change?
Altering our habits makes us uneasy; it takes some time to adjust. Your perseverance is laudable, and pursuing DevOps as the next level of team collaboration is often the right choice.
There is no need to give it up altogether; perhaps put it on hold for a moment.
Look around you. Those faces, those different personalities, can you picture them all together singing Kumbaya? Maybe yes, maybe no, or not yet.
Please do not e-mail an anonymous staff survey. Get everybody in a room, lay your DevOps propaganda out, and gauge their reactions.
You will need everyone to fully understand the concepts, acknowledge the challenges, and accept the sacrifices for this to work. There can neither be exceptions nor ambiguity.
All of this requires a great degree of cultural change, which a team should be prepared for.
What would it take to change the current mentality? How much of a disturbance you would need to cause? What degree of backlash do you expect?
While I am not suggesting this as an excuse to put up with the status quo, I beg you maintain a pragmatic view of the situation.
Your type of organization might be better suited for a process of evolution rather than a revolution.
How would you score your current processes? Would you say your cross-team communication is satisfactory? You regularly meet business expectations? You have already automated most of your workflow?
It sounds like you are doing fine as it is; you might already have some DevOps in your team without realizing it. The point is that it could be a better use of resources if you were to concentrate on optimizing elsewhere, solving other, more pressing problems at this time.
Now that you have been through a yet another interpretation of the ideas behind DevOps, if you feel those match your way of thinking and the final few questions did not raise any concerns, then we can safely transition to the more technical topics where we put principles into practice.