They are uncommon, but not particularly rare from what I have seen. Maybe 20% of the 1903's I encounter are Mk1's.
Damn few good 03's here...I know, since I collected Springfield Armory stuff for about 20 years. I had 6 1903's of which I kept 3. The ones in the rack are;
-Rock Island Arsenal, 5 digit serial, 1918 RIA barrel, DAL stamped stock.
-Springfield Armory, 6 digit(260,###), 1918 SA barrel, double stamped stock(script and block).
-Remington, 3,2xx,###, 1943 RA barrel, FJA stamped stock...no it is not the finger groove stock ala '03A1 type...I only wish.
-Remington, 3,2xx,xx, M1922 sporter clone, original m1922 barrel band, Redfield peep sight, 1944 RA barrel...this is a fantastic shooter.
Years ago I sold my MkI and a WW2 rebuilt SA(had the scant grip stock)...kind of sorry I did though since they would still be welcome in the rack.
At last years Portland OR show I was helping a buddy from Montana with his display of an original complete m1903 periscope trench gun and his complete Pederson device, and MkI rifle and accessories. Imagine a sealed 400 round carton of 30 Pederson Frankford arsenal ammo, plus the functional Pederson device with the metal carry case and 8 original magazines. Needless to say he won best of show. It also helped that he had the 1913 patton saber with the M1911 mounted in the basket hilt...yes, it is the one shown in Canfield's book on U.S. Infantry weapons of WW1.
Cheers