Analog computers are often faster and even more accurate than binary computers on the same problems. The major problems are of reliability of the parts, reproducibility of results, precision (rather than inaccurate answers with good precision they tend to give accurate but imprecise answers), program flexibility (most are designed for the task at hand), space, and cost.

Next to using quantum effects, inserting analog components at just the right part of a computing task might be the best we can do. However, the costs associated with analog computers tend to relegate them to curiosities or simple, fixed applications (like the bimetal thermostat).

The real strengths of binary digital computers are low cost, compact size, and flexibility of purpose. If we could have a reliable multi-state logic gate that fit in the same space as a binary one, cost as little to produce, and took no extra power then that would be great. So far, though, the ranges of voltages idea hasn't been reliable enough. Anything that requires extra hardware for a third state could just as well be used to produce another binary gate.

The same things that are great about binary systems are the things that limit them: smaller, cheaper, faster, more flexible. Your program's logic doesn't need to be limited by the binary nature of the hardware. You might pay an extra cost in memory use by using multi-value logic rather than boolean and you might lose some efficiencies that were offered for Boolean tests. Many things that are less efficient in some way are still worth using, though.

The use of fuzzy sets, multi-valued logic, iterative adjustment of outputs, and proportional application of expert rules can make a control system much more regular than discrete Boolean branching. Folks making embedded systems for consumer products have been making strides in this area for quite a while. Zadeh's concept of possibility vs. probability changed the way I think not just about programming but about many things in the real world.