Part of his mandate will be to spearhead a renewed era of exploration into the Gamma Quadrant. Humans in the Trek universe can live at least 110 years, but it should be more. In the Trek universe, it IS more. Not so coincidentally, one of the new regular characters being introduced in the post-finale DS9 novels next May is a centenarian. But what you're suggesting doesn't sound unreasonable.
People age very differently in real life.
No reason they shouldn't do so in Star Trek too. A hundred years may sound like a lot to some, but this character is only two-thirds of the way into his natural lifespan, and he's lived the life of a Starfleet officer. No one should expect him to be using a walker. It only serves to annoy the audience when that rate isn't adhered to consistently. And Picard is over 70 by now, but he doesn't look anywhere near that old.