If you don't have a lot of tire clearance I would worry about picking something up in the tread and having it jam between the caliper, fork or stays and tearing the tire or locking the wheel.

I had this happen once and it was pretty scary... I flew off the seat onto the top tube/stem, both feet forward and slid to a stop on my heels (road shoes) from ~20mph. Found my front tire had picked something up and it had jammed between the caliper and tire and locked the front wheel. It was one of those anti-theft dye packs they put on garments. Apparently it had been on the road lying nail side up and I rolled over it dead center (what are the odds?). The tire (23mm slick) had plenty of caliper clearance but it was a big object. This happened ~5yrs ago and I still have the dye stains on the socks I was wearing from wiping my hands off after pulling it out of my tire. I curse that shoplifting litterer to this day...

With the clearance you look to be running along with the tread it might take something smaller to put you in the same situation...