Of course you won't go out with cold tires with u have a choice.
When you can push hard and the tire becomes over-inflated and thus loosing grip because the contact patch between road and tire is reduced.
Moreover, when it starts to rain and safety car comes around, the tire loose pressure and thus looses structural strength.
you will have less worry about it with this tech.
I think F1 teams can debate this in terms of safety aspect.