I too think it depends on the size and use of the counters. I find that small, flat cardstock counters are difficult for me to organize, handle and manage as a game goes on.  I have switched to small and tiny colored dice for almost everything that a numerical counter is used for, and for markers that have an image I always mount them on a backer/base. Real small markers or counters are much more difficult and tedious for me to mount so I might skip them completely. Pre-cut may help a bit with that. 

Larger "ship counters" I wouldn't mind cutting out of a sheet, but I would still probably mount them to something else to add some depth to grip.

I guess I would like to know what the precut counters would be made of. If they're just perforated cardstock (I think some of the B5Wars game supplements came with these) I wouldn't be as excited about them as if they were die cut out of some nice thick material like the games of yore I'm having flashbacks to sorting Avalon Hill Blitzkrieg pieces.

To sum up: Uncut card is ok with me if the counters are large enough. Precut would definitely be preferred as an option if they are made from quality material, but not required as standard if they drive the price of the game up too much by their inclusion.

That would fall under the latter half of my prior answer then.

Which would work fine if printed on decent cardstock then glued to foam core squares. Some might think Sticker paper would be easier...but my experience with this method has the stickers peeling up over time as the adhesive used fails with age. The foam core makes things easy to pick up and is nicely durable. I still have and use the counters I made that way in the early 90's in near mint condition as it were.