Yep, the problem is that the 2-4 cc hunk isn't going to last very long. Maybe a couple of days...maybe. And in order to have it even last that long it would have to be inside some kind of pressure vessel that could control the rate of sublimation. Sure, you could just gas it off, but that would waste a lot of co2 and therefore a lot of dry ice.
Additionally, the temperature of the gas bubbling into your tank is going to be very cold. Dry ice sits about - 78 C. The gas coming off is going to be cold and is going to cool down your tank, a lot.
If it were to be inside a pressure vessel, that vessel would have to be inspected in order to be safe....and at that point it's just a regular ole' co2 cylinder.
Aside from the temperature issue, it can be done, but it's terribly inefficient if it's not in a pressure vessel, and if it is in a DIY pressure vessel, it's terribly unsafe.
It can be done, just like breathing into a trash bag and releasing that into your tank throughout the course of a day can also be done.
The initial startup cost of a pressurized system seems daunting, but it really is the cheapest and most efficient method.