Are you supposed to do it or not? What are the benefits / downsides?
Placing your HQ on top of resource tiles has the following effects:
You immediately receive a quantity of these resources.
Quantity appears to be currently 20 for each low tile covered, 30 for mediums, 40 for highs.
Note that Robotic HQs receive twice as much as the other HQs.
Those tiles not available to use for the rest of the match.
The latter could be a downside if you didn't choose your location carefully, otherwise I would say that you almost always want to place your HQ on some resource tiles to get yourself some free starting resources.
Unless you completely cover a section of a resource, doing this will also allow you to then place extraction buildings for that resource adjacent to your HQ, avoiding transportation fuel and time costs.
Finally, there's also a possibly that you can block access to resources your opponents might need or want (for example, covering up good water sources if you're going in as Robotic might be a worthwhile tactic if water is sparse).