As always with the 17hmr caliber, the limitations are with the ammo. The ammo can vary a great deal. There's no 17hmr ammo equal in quality to top-of-the-line match ammo available in .22LR.
As with other rimfire calibers, 17hmr ammo quality varies by manufacturer and by lot.
One potential problem is a potential lack of MV consistency. It's not unusual to see extreme spreads of 150 -200 fps. Such high ES figures have more obvious implications for longer range shooting than for shorter distances.
Hummer ammo can have two more serious problems. They are inconsistent bullet seating depth and roll out, the wobble in a bullet that is not aligned by its axis. Sometimes this wobble is great enough to be visible when rolling the cartridge on a smooth, flat surface. Both of these problems can contribute significantly to results downrange.
The results of these problems are shown on the RFC thread that compares chronographed results of 50 rounds of various 17hmr ammos (as well as other rimfire calibers) shot at 200 yards. For more, see h t t p s://www.rimfirecentral.com/forums/showthread.php?t=1129343 -- scroll down to the bottom of the page for 17hrm ammos.
In the end, accuracy is largely the result of the ammo quality and barrel quality. While it's unclear whether among the rifle makers there is any variation in the 17hmr chambers as there is with .22LR rifles, the barrels on each manufacturer's 17hmr rifles will vary in terms of potential accuracy. Most will be average for that make of barrel, a smaller number of them will be better or worse. For greatest accuracy, the better odds are on a barrel made to the highest standards available. Of course that will be more expensive, and every shooter has to find a rifle that fits his budget and requirements. Fortunately, there are many rifles from which to choose.