The only problem with ECC is that it is only an improvement, not a solution. Every error correction has a limit to the number of errors it can detect or correct. There is no such thing as absolute security.
Having a small remaining probability of error is not a problem at all, if it's small enough. There are always potential sources of failures (such as a meteorite crashing on your server). If the probability of one source is dwarfed by others then it doesn't matter.
It's not a "problem" if, as you say, perfection is an unreachable goal. The only question is whether it's an improvement over the status quo, and it clearly is.
