The main objection is not about Cena, it's about remaking a classic film. The first Terminator movie was a gritty horror movie that was a product of its time. If it was made today it would be too glossy, bright and clean.
Regarding Cena as the Terminator, I don't think he would work. He has this goofiness about his charisma that lends him to be better with comedy. You are just looking for a big guy to be the Terminator to replace Arnold but that's not what made him good in the role. The second best Terminator was Robert Patrick. He wasn't a big guy but he was able to play that focused, stone cold killer role while switching it up when infiltrating to get information on his target and he made it believable and frightening. It seemed believable when he was tossing Arnold around in their fight because he made you forget he wasn't really a machine. That's how a terminator should be and I don't think Cena could pull it off.