For one, the player's willingness to take on one last challenge in his career suggests that there's no shortage of motivation or self-belief. And no club as ambitious as Roma would take a chance on a player they believed was past it—so they obviously believe the ex-England international still has much to offer.
There are few operators in the transfer market than the Giallorossi's Walter Sabatini, and his endorsement alone should be enough to silence the detractor because the 59-year-old Perugian is rarely wrong.
Sabatini has a long list of stars he can point to as evidence of his ability to unearth talent, but his success hasn't always just come with young players. Last summer, he saw more in Udinese's 26-year-old Mehdi Benatia than anyone else, and when asked by Rudi Garcia to bring Gervinho to the Italian capital from Arsenal, he ignored the common consensus that the Ivorian was useless, only to be repaid many times over by the explosive forward's rebirth in Rome.
More relevant to Cole, however, are another two astute, bargain moves for unwanted players he made that transformed the squad.
Maicon and Morgan De Sanctis—who'd both been written off by their clubs and by most fans and commentators as too old—were brought to the Olimpico, and both excelled. Cole can do the same because there's clearly a culture of meritocracy at Roma, and even though he's 33, if he trains hard, he'll know that he will have the full support of the club and as good a chance as anyone to start.
Cole will have had easier options. He could have followed Frank Lampard to MLS or taken a huge contract in Asia or elsewhere and simply allowed his career to fizzle out. Instead, he's chosen to prove that he's still got what it takes to make it in a major European league—and taken on a challenge that few other English stars have been willing to risk.
With the very brief and ineffective exception of David Beckham's loan at Milan, no Englishman has graced a Serie A pitch since Jay Bothroyd played for Perugia from 2003 to '05. He's faced with a new culture, a new style of football and a new language—so he's clearly still hungry.
Speaking to The Guardian, Cole was clear about his desire to do well in Italy.
English players feel in their comfort zone in UK. This is a chance for me to try a different language, culture and way of living.
As soon as I spoke to Garcia and I saw how much they wanted me here at Roma I jumped at the chance. I've always had a good relationship with Jose Mourinho, but I was no longer useful to his project at Chelsea.
I came here to play in the Champions League. Roma is an ambitious club, it's a challenge for me and I'm prepared to fight for my place. Hopefully we can do something special here next season and win Serie A.
I'm not afraid of pressure. I noticed the fans' passion and love as soon as I landed. I'm going to enjoy my time here.
Throughout his career, Cole's never given less than his best. At both Arsenal and Chelsea, he was an essential component in their success—three league titles and seven FA Cups—and perhaps more important than that, he's one of the rare examples of a modern celebrity English footballer in the Premier League who's actually fulfilled his potential and become truly world class.
Cole has been the paradigm of a left-back for the last decade at both the club and international levels, and if he starts the season fully fit with Roma, he has a legitimate case for being called the best in his position in the league. He is perhaps just past the true apogee of his talents, but he's still immensely talented and comes with invaluable experience—two characteristics that will make him an important point of reference for the Giallorossi this season.
He won't be long in the Italian capital—but he should leave a lasting impression.