On the whole, I agree with this. I pay for a very subsidized lunch with my work badge (yay for software companies!) and what I really need from my purse = keys and security card.
However, I know people at my company who go wallet free. Not a single one of us really needs more than our car keys/bus pass/bike lock key, house key, and employee badge. The problem that I've seen people run into is running out of gas. I work in the southwestern suburb of a college town/state capital, and cars are necessary to pass the cornfields. Running out of gas wouldn't happen to someone taking the bus or walking to work, so that's specific to car-centric areas. My officemate spotted her besty $20 so her besty and her besty's husband could drive home. "They're such smart people! How can they not have ANY money? They both left their wallets at home!"
My advice would be to keep a fun fifty designated for having fun with friends/cash emergencies (like being unable to get home) hidden away at your desk. You may differ, but I find it difficult to make careless purchases with cash, especially a pristine 50. [I actually find it very difficult to spend physical cash, but that's another story.]