Wheat next to a river is one of the only resources I would never settle a city directly upon. There must be a nearby tile that is almost as good to settle upon and keep the wheat tile for a farm.
There's no problem in general with settling on luxuries or strategic resources (every situation is...well, situational ). But you might need a corresponding tech to access it, like Calender or Mining etc.
One of the best locations I see is next to a river on top of WHEAT.
Is there a downside to building on top of a resource?
On Deity I will usually settle my first (often only) city on top of a luxury resource, preferably a mining one on a river.
Having 450g+ on turn 15 often means you can have both a Library and Granary up for the turn writing is finished (tech mining, pottery, writing) which enables you to have your city production focused for NC building and still grow (slowly).
Thats just my first city, further settled cities employ a more long term focus so I will look for ideal city placement (food, hills, # of luxuries closeby etc) which usually will not mean settling on top of a luxury resource.