"We need guys who are fresh... alongside performers who know how to get the job done," coach Hesson said. "We lost a lot of experience post World Cup and we can't just replace that with promising new guys."
Broom would be the unanimous choice as man-of-the-series.
He made his maiden ODI century, an unbeaten 109, in the second match, a game where Bangladesh's Imrul Kayes was the only other player to score more than 40.
Broom followed up on New Year's Eve with 97 off as many balls in a 179-run stand with Kane Williamson, a record for New Zealand's second wicket against all countries and a best for any partnership against Bangladesh.
Earlier, Broom kept New Zealand in the contest when he executed one of the catches of the summer. Bangladesh were 102 without loss and Imrul miscued a slog sweep. Broom sprinted 15m to his right from short third man and threw out an arm. The ball stuck.
"It's difficult [for Broom] replacing a quality player like Ross [Taylor]," Hesson said. "You could feel like you were on borrowed time, but we needed an experienced player capable of playing a variety of innings.
"He's done everything we could have asked and probably more. In two situations we were under the pump losing regular wickets.
"His energy fielding at backward point created opportunities, too. He's 33, but a young, fit man who's hopefully got plenty of international cricket ahead."
"He was relaxed [to bat with]," Williamson added. "He's scored a lot of runs domestically around the world and in county cricket, but is a much better player than when he made his debut. He stood up to play two mature innings."
Patel was selected for the final match as New Zealand sought to capitalise on footmarks when turning the ball away from the three left-handers in Bangladesh's top five.
It followed his recall to the test side in October having played as Warwickshire's pro for years.
Patel took one for 40 from his allotment and showed a safe pair of hands on the boundary.
"The way Jeetan bowled, when it was hard to play across your front pad, created enough dots and indecision," Hesson said.
"We've been considering using Jeetan as an ODI option since India but he was unavailable against Australia because of the arrival of a baby.
"We'd potentially keep him in mind for the Champions Trophy [in England] where we will take two spinners and play on surfaces Jeetan's familiar with."
Hesson said opportunities to play two specialist spinners were rare in New Zealand. The third ODI offered a chance to get him in the mix and see how he operated.
"He did exactly as we hoped. You can put him on autopilot and he goes out and does the job. That's a skill you can't overlook."