Headshots are completely up to you - you can have none in your database if you prefer. It won't affect any profiles in relation to the online database.
For the custom headshots that are stored outside of the actor's database then I believe you can simply delete the folders inside the CreditPhotos folder. Unfortunately I can't think of an easy way of removing the standard headshots that are stored inside the actors' database, though hopefully someone else can.
As always, when deleting stuff like this I'd recommend you perform a backup first.

The cover images are space intensive. (At my database: 1,5Gb of 2,7Gb)
Actor/crew headshots seem to be saved in actors.blb. This was the biggest file at my database with ~680MB.
I don't think this is too much space, but if you still want to delete the headshots in your database you can do this (for those not in your database) with a database repair. (Preserve Images or similar. And if I remember correct there is also a way over doing a restore from a back up)

If it is just the place that you don't like: You can make a new database in a different place/hard disc. (at "open database")

I went ahead and deleted all the cast/crew from all DVDs in my wishlist. But after doing a repair I noticed that the amount of my databases had not decreased.

So I did a backup first, deleted all my databases, including artwork and then re-started the program and did a database restore.

I re-downloaded the artwork and re-looked at the amount of space the program was using in the dvdprofiler folder and it decreased by well over 200MB.