I have wondered about this before. He makes no mention of having any sort of implant and usually dresses very casual other than his helmet during missions.
Ingame i like to think this is his personal preferences plus lack of money to buy more expensive equipament.
Out of game i get the feeling maybe this is a way to make Jake, Sonya, Tex more distinct as characters.
Not just more distinctive, but also more defined. The faceless ghosts get bulky armor to make them look disposable but still a bit intimidating. Tex gets the cowboy look to suggest he's eccentric but rugged. The MC gets simple clothes to appear relatable and outmatched. (And to explain how he can take them off so fast if a femme fatale stops shooting, of course!)
In game, I can see two possibilities. The first, as you mentioned, is that he no longer has money for the good stuff so he prefers to maximize his mobility. The armor on the ghosts doesn't seem to do much against his gun.
The second is that he actually is wearing armor, it's just sophisticated enough to look mundane. In this scenario, he bought it back when he had a regular income and spent extra avoid attracting the attention of bulky combat armor. It probably wouldn't stand up to heavy ordinance, but could deflect the small stuff; his missions seemed to be more about kidnapping rather than straight up combat, after all.
Given that we know he still has access to some apparently cutting edge munitions I'm inclined to believe the second option, but either option is plausible.
