Yes... but nobody uses binary systems. We use 64 bit systems (and a number of other systems, but all larger than one bit), which has abundantly more than enough space to represent "greater than/less than/equal".
The main software issue with ternary computing is that with this, the entire advantage goes up in smoke. It is quite hard to articulate an actual advantage a multi-bit system would see since we do not use 1-bit or 1-trit systems in real life. (If you've got some particular small hardware thingy that could use it, by all means go for it; it's no problem to use it in just one little place and have a conventional binary interface.)
Taylodl's hardware issue with ternary circuits sounds like a reasonable one as well. If you've already minimized the voltage difference for your binary circuits to as small as it can reasonably be, the addition of ternary hardware necessarily entails doubling it the maximum voltage in the system.
Is this Quanta Magazine's "Brash And Stupid Claims About Computing Week" or something? https://news.ycombinator.com/item?id=41155021 The last paragraph is outright crockery, that "trit-based security system" is well known to be from a crackpot who appears to simply not comprehend that our binary systems do not in fact explode the moment they have to represent a "3", despite repeated attempts for people to explain it to the guy.
Programmers and hardware designers are not in fact just total idiots stuck in the mud about digital (vs analog) and binary (vs ternary) representations. They are the way they are for good and solid engineering reasons that aren't going anywhere, and there is basically no space here for someone to displace these things. It isn't just path dependence, these really are the best choices based on current systems.