We live in downtown San Francisco and get our organic produce delivered weekly from http://farmfreshtoyou.com
We've been using it for more than a year and have been happy with it, that said I'd be curious to hear other suggestions, specially services that deliver organic produce from a group of farms instead of only one.
Frankly vegetables and bread are the main thing I would want delivered quickly and often - pantry staples I can stock up in one big monthly trip, it's not really a big deal to fit that in.
Instacart also makes a lot of sense in groups, where no one individually wants to be responsible for going for stuff. Parties, roommates, or offices.
The problem with fish/produce/etc. is there's variation on offer. If I go to the store and want some tuna steaks, but see hamachi is on sale, I might get that instead. It would be hard to delegate that level of decision making to anyone who wasn't a routine agent, or having an exceptionally good CRM, or having a realtime inventory system at the store.
What I'd love if if someone could get Tokyo Fish Market in Berkeley, a few farmers markets, etc. to publish realtime inventory info, and do a buying trip once a day. Go in in the morning, see exactly what is there and at what price, let me know, and then I'll let you know in an hour or so what I'll buy. Specialized restaurants do this already (e.g. sushi chef goes to the fish market), but maybe smaller places would be more likely to do it for ancillary items if they could use tech to do it for them, or home cooks would do it. Most restaurants just use food service companies like SYSCO for most of their stuff now, though.