It might be "nice", but it's not possible without a very restricted definition of "every amenity" and even then there's an assumption that amenities are fungible and you're ignoring efficiency.
If there's a grocery store every five minute walk, it's relatively small, which means that it has a crap selection AND it's expensive to run because it doesn't have any economies of scale. (Compare NYC's bodegas with even a crap Walmart and god help you if you're not the dominant community near your bodega.)
The number of places to eat/drink within a five minute walk is limited and/or they're tiny. Again, crap selection and no economies of scale.
Then consider our musician friends. Do you really think that NYC supports enough instrument stores to have one, let alone a good one, every five minute walk? (Remember, you need guitars, flutes, pianos, etc.)
And, musicians aren't special here - the same is true of any interest, such as books.