And the cleats don't stay 'recessed' for long because the rubber sole wears away whereas the steel cleat doesn't - how much of an issue that is depends on how much walking you do and what you're walking one.
However, for your work, I'd buy a pair of cycling shoes and use them on the bike, then carry a pair of trainers for use in the gym. No, I'm not a huge fan of carrying stuff around that you shouldn't have to but in this case, I'd put your footwear in the same category as a pair of neat trousers for an office worker.
Richard