Starc's 19 wickets from seven matches, more than any bowler in the tournament, have been instrumental in Australia booking a place in the last four with two group matches to spare.
The defending champions can afford to rest Starc or Cummins, who has 11 wickets, but Finch does not want to mess with a winning combination.
"So if it was going to happen at all, yeah, slightly tempting, but at the same time, you don't want to tempt fate," Finch told reporters at the Lord's.
"You don't want to upset the apple cart just for no reason, really. And that also comes down to how they are feeling, as well, and they are both feeling great at the moment.
"I know that they have got no interest whatsoever in being rested or anything like that... everyone's really on the same page in that regard -- to try and keep our winning momentum and making sure that we are never taking anything for granted in this tournament."
Australia finish their group campaign with a July 6 match against South Africa and Finch felt the gap between the games was enough for the quicks to recover.
"We feel that week will be a really good opportunity for the bowlers to really freshen up and de-loading them three or four days after this match to manage them through the next part of the tournament, and obviously with a huge summer coming up here with the Ashes and all going forward."
Saturday's contest will be a rematch of the 2015 World Cup final when New Zealand were shot out for 183 and Australia chased down the paltry target with nearly 17 overs to spare.
Finch had no doubt, however, that their trans-Tasman rivals under Kane Williamson will fight tooth and nail.
"I think the great thing with New Zealand is that they fight and scrap every single game, regardless of whether it's a World Cup final or it's a club game," Finch said.
"That's a part of how they play their best cricket, and I know under Kane they certainly do fight and scrap for every run on the field.
"They are a great fielding side. They put pressure on you. They have got world-class players. It's going to be a good game tomorrow, no doubt."
(Reporting by Amlan Chakraborty in Birmingham, editing by Toby Davis)
